Beetlejuice (NES)/Any%

Inventory management

Items in the inventory carry over between levels. There are different alternatives for how to manage the vouchers (for buying scares in the side view levels) and potions (for defeating enemies in some of the rooms in the overhead levels). It's therefore worth some additional discussion to go through the considerations behind the one shown in the route described on this page.

Vouchers

Name	Vouchers	Accumulated	Comments
Key (outside the house)	+75	75
Book (house)	+75	150
Fly in the clouds (village)	+75	225
Beetle	+25 (or more)	250	If you get 75 vouchers or more (so by stomping on a yellow beetle or by stomping on several beetles), you have the option to do different purchases in the shop in level 2. By getting 100 vouchers or more, you can skip jumping on the fly in level 2. Both of these are roughly 1s time saves, so not worth doing any big detours for, but still worth consisering since the beetles sometimes align so it's possible to get additional vouchers for a very small time cost.
Skeleton scare (shop)	-250	0	(In practice) mandatory to proceed
Fly (raft section, storm drains)	+75	75	If you managed to get at least 100 vouchers outside the shop in level 1, you can take a hit against this fly instead of jumping on it. The time save in that case is a little over a second.
Extra life	+75	150
Free umbrella scare (at the 1st cavern monster)	+75	225
Defeat 1st cavern monster	+7x75 = 525	750
Free umbrella scare (at the 2nd cavern monster)	+75	825
Defeat 2nd cavern monster	+7x75 = 525	1350
Buy scares - option 1 (after the 2nd cavern monster)	-1x500-1x400-3x150	0	One ogre, one umbrella and three birdman scares. This requires two shop visits.
Buy scares - option 2 (after the 2nd cavern monster)	-2x400-4x150	-50	Two umbrella and four birdman scares. Instead of using the ogre scare against the third cavern monster and the boss, like in option 1, first use an umbrella scare and then a birdman scare. This option requires an additional 50 vouchers. There are several possibilities for this. For example killing more beetles (or be lucky to get a yellow one), jump on another fly or get it unintentionally by getting hit by the cavern monsters to get more free scares (each one worth 75). Since the purchases in this option can be completed in one shop visit, around 3 seconds are saved. However, the third cavern monster will have to be defeated by 7 shots from the umbrella scare instead of one shot from the ogre in option 1, which loses some time and adds a bit more risk. Finally, another menu trip to equip a birdman scare is required against the level 2 boss. Overall, option 2 can be expected to be around 1 second faster than option 1, but also adding a bit more risk.
Buy scares - option 3 (after the 2nd cavern monster)	-1x400-6x150	50	One umbrella and six birdman scares. Use the umbrella scare on the third cavern monster and the remaing attacks plus a birdman scare against the boss. In the graveyard, use three birdman scares against the boss. The advantage with this option is that it only requires one shop visit, without relying on getting additional vouchers. As an optional bonus, if 25 more vouchers are collected, the 75 vouchers from defeating the fly at the start of the stormdrain level aren't needed, saving around one second. There are however a few downsides with this option. First, by not having the ogre scare, the third cavern monster fight becomes less consistent. Secondly, there is no option to take an intentional damage at the end of the graveyard stage to reset Beetlejuice's health. Finally, there is less room for mistakes against the third boss. Time-wise, this option should be a few tenths faster than option 1 (add around one second to that if the fly at the start of the stormdrain doesn't need to be defeated). Around 3s are saved by only visiting the shop once. Around 1s is lost against the third cave monster. Just over a second is lost from a menu trip in the second boss fight and the same from an additional menu trip against the third boss. Finally, by not switching between birdman and umbrella scares in in the menu in the last levels, like in option 1, option 3 saves a few tenths of a second.

Potions

Room # (see $55)	Potions	Accumulated	Comments
8	+1	1	Can in theory be collected without time loss, but will in practice likely be a few frames slower. However, by delaying 15 frames, the second buzzsaw (?) can be avoided, which is a good trade-off. Collecting the potion within this delay should not be a problem in real-time.
9	+1	2	On the way. Another potion just to the right can be collected for a cost of ~80 frames, but is not recommended when attempting an optimized speedrun.
B	-3 +3	2	The potions are used in a semi-random fight with sweepers. Using 3 potions is a realistic goal for a good fight, but sometimes more will be required. It's usually possible to collect the 3 potions in the upper right room without time loss.
D	-1	1
E	+3	4
F	-1	3	It's debatable if one or two potions should be used in this fight. Partly it depends on how the art pieces move, partly personal preference.
0x10	+1	4	Beetlejuice will very often take two forced hits in this room. If that means Beetlejuice is down to his last health, the auto-scroller in the next room can be risky to get through on the right side and it might in that case be worth taking an additional third hit (or taking the left path in the next room). If there had been a good opportunity to use a scare to get past the footballers' legs, it would have been worth it. The problem is that there doesn't appear to be a consistent strategy for it.
0x11	-1?	3	Throwing a potion here is far from a guarantee to avoid taking any hits. At least if the sweepers are separated, it's probably worth using a potion since there is otherwise a increased risk of taking two hits in this room.
0x12		3	The potion below the fly swatter is ~40 frames out of the way. Out of the optional potions not collected in the route shown on this page, this one is the least out of the way.
0x14	-1	2	It's common to take a hit at the start of this room, which will usually mean one or more legs getting stuck around the exit and a forced second hit. By throwing a potion, the first hit can often be avoided and it's less likely for any of the legs to get stuck near the exit. As a rare bonus, it potion can even kill one of the legs and thereby create a chance for a beetle. It's therefore recommended to use a potion in this room.
0x18	-1?	1? or 2?	It's common to take two hits by the legs in this room. Using a potion can usually avoid one hit, with a rare chance of even killing the legs and getting a beetle). The difference between using a potion in this room or in 0x11 seems fairly small, so it might in the end be a choice of personal preference.
0x19		1 or 2	There is an optional potion in the top right corner, which costs ~70 frames.
0x1D	-1? or -2?	0	Using one potion is risky, but a fairly significant time save (a little over 6s). Two well thrown potions are however almost guaranteed to take out the sweepers. Saving a potion in this room could also open up for another potion use earlier on, e.g. in room 0x18, leading to another potential (minor) time save.

Level 1 (Village)

Outside

https://vimeo.com/810446088

It's theoretically fastest to collect the key while jumping away from the cloud. However, the time difference between the different ways to collect the key are likely going to be overshadowed by execution inaccuracies. But on average, it should be a few frames faster to jump later from the bush to the cloud than landing too far left on the cloud and having to start with a more vertical jump to collect the key.
The jump to the door is optional. However, since the x-speed is constant and "up" can be buffered during the jump, potential time losses from moving the thumb from "left" to "up" on the d-pad are eliminated by jumping instead of running to the door. The door can only be entered by standing on the ground though, so jumping does introduce an unknown factor in the form of air time.

House

Since the cloud elevators run on a fixed timer that starts when entering the house, the route can be adjusted to the possible cycles. Each cloud cycle is ~3s and the difference between an "early" and a "late" cycle is around half of that. The fastest way to get through the first section of the house is on a "late" 5-cycle cloud elevator:
https://vimeo.com/810479987

Requires a flower at the first switch
Requires "good" light light timer in order for the third lamp to be unlit when passing beneath it
Requires somewhat tight timing when flipping the first switch or you won't make it back quick enough to catch the first cloud elevator in the "early" 3rd cycle
Requires tight execution to catch the second cloud elevator in the "late" 4th cycle and the third cloud elevator in the "late" 5th cycle

Overall, most players will probably have a low success rate with this route since it both requires good execution and luck in a few places. If the third light is blocking the path to the first switch, it's probably going to turn into a 6-cycle (so roughly 1.5s slower). As an alternative if the third light is blocking, one can damage-boost through it as well, which will also result in a 6-cycle cloud elevator:
https://vimeo.com/810480077

Requires a flower at the first switch
Damage-boosting through the third light makes it impossible (?) to catch the first cloud elevator in the "early" 3rd cycle, which means the execution on the ground floor doesn't have to be anywhere near as tight as when attempting a "late" 5-cycle.
Catching the first cloud elevator in the "late" 3rd cycle isn't too difficult, but still requires fairly precise inputs. The second and third cloud elevators are easy to catch in their respective cycles though.
Jump from the last cloud elevator directly to the cauldron (and not to the floor) to avoid an additional jump

The following link demonstrates a possible outcome ("late" 6-cycle) if you don't get the flower near the first switch:
https://vimeo.com/810480020

Requires the light before the second switch to not block your path for too long or you won't be able to catch the second cloud elevator in the "late" 5th cycle, which would in turn make a "late" 6-cycle impossible.
The fish in the cauldron before the second cloud elevator is a risk factor that can't be controlled without the flower invincibility

It's possible to do a 6-cycle even without a flower, but it's unlikely since it requires almost perfect timing of the light before the second switch and luck with the fish in the cauldron right after. Even a "late" 6-cycle requires both fairly tight execution and luck in some spots. It's much safer to aim for a 7-cycle without the flower.

The last section of the house involves getting rid of an "urn with a bouncing smiley" that blocks the exit. If you got the flower before collecting the book, the urn can be ignored and it's only about flipping the two switches on either side of the exit. Note that the weight falling down when flipping the first switch needs to disappear off-screen before the second switch can be flipped. Without the flower, some time-consuming dodging (usually ~1.5s) is required both after flipping the first and the second switch to safely exit. The videos above demonstrate both of these cases.

The mechanics of the exit might not be evident from a glance and are worth studying a bit more in detail. The exit is triggered by Beetlejuice touching its hitbox (no need to press up or other input). The following is an illustration (not pixel-perfect) of the exit's hitbox with respect to Beetlejuice's shoe soles (y) and his centerline (x):

If Beetlejuice has flower invincibility, he can just run into the hitbox from the right without issues. Running into the exit without invincibility will stop Beetlejuice at the rightmost pixel of the hitbox and he is almost guaranteed to be killed by the smiley. However, if Beetlejuice is in the air, he will not stop his movement, but will still trigger the exit. There are a few ways to achieve this:

Make a small jump before the hitbox
Drop through the floor and let the momentum have Beetlejuice trigger the exit
Make a big jump both flipping the second switch and then land inside the hitbox

'1' and '3' work when the smiley is around the urn. '2' works when the smiley is above the platform. In practice, it might be easier said than done to assess the situation and decide on the correct input, but it's at least possible in theory to react to the smiley. By exploiting the hitbox in this way, the last part of the house can be cleared without time loss, essentially making the second flower optional.

Village

https://vimeo.com/810530071

25 vouchers will be missing to buy a skeleton scare in the shop. The only reasonable way to get them is to stomp on beetles. Either three red ones (worth 10 each) or (preferably) one of the three more valuable types (worth 25, 50 or 75).
Note the comments in the voucher section above about possibilities in case more vouchers can be had for only a minor loss
Note Beetlejuice's position when waiting for beetles to spawn. When standing in this position, beetles spawning from the left hole will generally be in reach (and they will spawn on the right side of the hole). Beetles spawning from the right hole will quickly despawn if they jump right, but be in reach if jumping to the left, towards Beetlejuice.
All the inputs in the shop for buying the skeleton scare can be buffered.
Beetlejuice exits the shop with the same x-position he entered it on and there is only one set of scares available in this shop, so it doesn't matter which pixel Beetlejuice enters the door to the shop on
The boss is not consistent in a speedrun and requires good RNG. With only three scare attacks to deal with the boss, there is no alternative to playing aggressively. There are still a few different possibilities on how to approach the fight:

Run right as the fight starts and attack once when in front of the right side of the fireplace. Then quickly stop to halt the x-momentum. Short jump to the right (anticipating jumping over a potential attack from the boss) and then two more quick scare attacks. (this method is shown in the link above)
Very similar to the point above, but jump to the right with full momentum after the first attack and adjust momentum mid-air so you land in front of the boss (and not crash into it)
Ignore what the boss does and try to do three consecutive attacks without any jumps
If the boss attacks shortly after entering the room and it's a "fast" attack, Beetlejuice can start by jumping over the attack and then hit the boss three times with scare attacks

'1' and '2' are close in terms of speed, so it's more a matter of personal preference which one to use. It's not trivial to calculate the success rate since there is quite a wide distribution of possible timings and shot speeds of the boss's attacks. However, disregarding execution mistakes, it probably lies somewhere between 1/3 and 1/2. '3' is a few tenths of a second faster, but also the riskiest of the three. The fourth method is simply a result of the circumstances (an early and fast attack from the boss).

Level 2 (Storm drains)

https://vimeo.com/810559625

It's faster to take the first two (intentional) deaths by falling off-screen than getting killed by the octopus
At the second death, it's slightly faster to let the screen scroll up (like shown in the linked video), than to drop down off-screen as early as possible. The difference is only a few frames though.
The "intended" route after the first cavern monster is to continue up to the top of the level and then descend down to the second cavern monster. Manipulating the window position so Beetlejuice can jump directly right towards the second monster is a shortcut worth a 5 or so seconds and was found by 'bartaan'.
Note the free umbrella scare at the first two cavern monsters
The cavern monsters' attacks are random. More often than not, they will hit Beetlejuice during the fight. The further away Beetlejuice stands, the smaller portion of the attacks will hit Beetlejuice. Another mitigation is to take an intentional death by falling off-screen. The deaths of course cost time, but also ensure consistent fights. For demonstration, an intentional death is shown at the second cavern monster, costing ~2 seconds.
See the voucher section for a discussion about the purchases in the shop. In this shop, there are 2 sets of inventory on the left x-pixels of the entrance and 2 other sets on the right. It's the ones on the left that are needed (the ones on the right don't have birdman scares). The inventory sets alternate every x-pixel. So enter the shop, buy the scares from that inventory set. Exit, move 1 pixel and enter the shop again to buy the remaining scare(s). The following table shows the x-pixels of interest:

x-pixel ($3BE)	Image	Shop inventory	Comments
0xA7		-	Not in front of the shop
0xA8
0xA9
0xAA
0xAB
0xAC
0xAD			From this position and to the right, the shop doesn't have any birdman scares

This is the last shop visit, so vouchers are irrelevant from this point onwards
It's a 50% chance to jump through the octopus, not possible to control in real-time. However, remember to keep holding A during the knockback, to buffer the next jump.
Note the use of the ogre scare's special ability to kill cavern monsters in one hit in the last fight
It's possible to skip the cavern monster fights by not allowing the screen to scroll far enough. However, the boss door will not be open if not all three cavern monsters have been defeated.
The sub-routine for the boss results in a higher chance of an attack than the first boss, so it's unlikely to get a fight without the boss attacking. Like the first boss, the best case scenario is a 3-attack fight.

Level 3-1 (Basement)

https://vimeo.com/810571287

To avoid getting hit by the second buzzsaw, minimum a 16-frame delay is required. Taking damage is in average ~40 frame time loss (or more if it happens to incur another continue). It's therefore well worth waiting briefly to avoid the damage and the potion can then also be collected without time loss as a bonus.

Level 3-2 (Kitchen and living rooms)

The room numbers refer to RAM-address $55.

Room 9 and A

https://vimeo.com/810580644

Spider damage can sometimes be avoided, but often it's going to cost too much time to dodge and it's better to just take a hit. A second hit should however more actively try to be avoided. It's likely that Beetlejuice will take damage in room 0xB, resulting in a death if he already took two hits here in room 9.
There is an optional potion to the right of the one on the way, but it requires a detour of ~80 frames and is not recommended to grab

Room B and C

https://vimeo.com/811026314
The sweeper fight in room B is one of the critical points in a speedrun. While the sweepers' and potions' movements depend on RNG, they can be manipulated to a certain extent. The steps outlined below and demonstrated in the link are in no way guaranteed to work, but do exploit the game mechanics and have been developed to improve the chances of a successful 3-potion fight.

Most of the time, one of the sweepers will home in on Beetlejuice from atop the sofa group (like shown here). In that case, it's important to throw a potion and try to get past it during its invincibility frames without getting hit. If Beetlejuice takes a hit, the sweepers will move away from him, resulting in a time loss of usually a few seconds. Sometimes, the sweeper will be stuck to the right of the sofa. In that case, it's recommended to throw a potion in its direction when above the sofa. That potion is still likely to deal some damage to the two sweepers in the lower room.
The quick left-right movement after throwing the potion was to try and bait the sweeper to move left and out of the way from the corridor to the next room. The RNG-element to the sweeper's movement does however not guarantee for this to work.
Wait at the top of the narrow corridor to bait the two sweepers below to follow Beetlejuice. The third sweeper will at this point hopefully be stuck in the lower left corner of the room to the right. The chances of this being the case increases if Beetlejuice isn't positioned too far above the corridor. There is again an element of RNG here, which makes this step non-consistent and there is always a risk of one of the sweepers getting stuck in the room below or the sweeper to the right escaping pre-maturely and start chasing you.
The most common scenario is that one of the sweepers from below comes up through the corridor. Beetlejuice can absolutely not take a hit at this point (or the sweepers will all disperse in different directions, leading to big time losses). The recommended course of action in this case is to move to the other side of the table and use it to shield off the sweeper from below a little longer. At this point, the sweeper to the right is likely to escape the right room and start approaching.
There are two options for this step:
1. Hug the upper side of the table and throw a potion to the right (as shown in the linked video). Most potion trajectories will stay inside the upper left room, with a good chance of dealing damage to all three sweepers that should now be in the room.
2. Move down to the lower right corner and throw a potion to the left. Throwing a potion from this position will ensure that the potion scare's trajectory will always be inside the top left room.
  
  In the first case, it's important not to get hit or there is a fairly high risk one or more sweepers will escape to another room, again leading to (potentially huge) time losses. The advantage with option 2 is that if you manage to get there without getting hit, the potion throw will likely hit all three sweepers even before turning into a scare. And if Beetlejuice is hit when standing in the lower right corner, the sweepers' main movement direction will be away from him, so towards the top-left corner, where the potion scare will have a good chance of dealing additional damage. In summary, the position to throw the second scare from depends on how fast the enemies approach. The standard option will probably be case 1, but if there is an opening to reach the lower right corner without getting hit, it might be worth trying for case 2.
Move to the right room, preferably without getting hit (or risking the sweepers to escape into the lower room). While waiting for the second potion scare to exhaust itself, collect the three potions in here.
Unless the sweepers are already on the way after having collected the potions in the right room, align Beetlejuice with the narrow corridor to increase the chances of baiting them to get through the corridor to the right room
When the remaining sweepers are about to enter the right room, throw a potion from the position shown in the linked video. All potion scare trajectories thrown from here will stay inside the right room.

Room D and E

https://vimeo.com/811727407
The strategy in room D is to throw a potion to deal with the two art pieces on the left side of the room and then take care of the art piece on the right side with the hammer. Since the art pieces move randomly, there is no consistent way to do this. Often, you'll end up having to chase one or both of the left art pieces and finish the work with the hammer. In order to maximize the chances for the strategy to work, the potion scare trajectory needs to stay on the left side and not escape to the right. There seems to be at least a few options for this.

As shown in the linked video, move up to the hammer, turn left and throw a potion. Not all positions have been tested, but this general area seems to give very reliable results with the potion scares staying on the left side.
Throw a potion vertically from around the lower left corner of the carpet. Not all trajectories in this area have been investigated, but this seems like a consistent way to get the potion scare to stay on the left side. See the following screenshot for the general position:
As you enter the room, walk straight up (no sideways movement) and throw a potion from y-position 0xF1-0xEA. The table below details how many potion scare trajectories (out of 4 possible) that will stay on the left side for each y-position:

y ($3C1)	Left trajectories
0xFA	3
0xF9	1
0xF8	1
0xF7	1
0xF6	1
0xF5	1
0xF4	1
0xF3	3
0xF2	2
0xF1	4
0xF0	3
0xEF	3
0xEE	3
0xED	3
0xEC	3
0xEB	3
0xEA	3

As can be seen in the table above, the ideal position to throw the potion from is 0xF1, which will ensure the potion scare stays to the left (this postion is shown in the screenshot below). Earlier than that and many trajectories will include the right side, while throwing the potion later gives a 75% chance for it to say on the left.

Options '1' and '2' are fairly similar. A quick test of 20 throws with these options was done from save states on a Powerpak (all of them different ones). 7/20 throws with method 1 took care of both art pieces, while 10/20 throws with method 2 were successful. By only comparing 20 throws for each method, it might be misleading to jump to too far-reaching conclusions regarding which method is best. However, option 1 tends to cover more area on the left side, while most trajectories with option 2 move close to the NW/SE diagonal. Deciding on the throw depending on the art pieces initial movements could therefore be worth considering. If not, one can expect roughly a 1/3-1/2 success rate. '3' has the (slight) advantage of being thrown as early as possible when entering the room. However, with quite a few trajectories not staying on the left side, the success rate will most likely be lower than '1' and '2', which should be the preferred options.

A strategy that can make sense is to take an intentional hit to freeze the art pieces in place for a short time. If this is done before throwing the potion, it could even influence whether to go for option '1' or '2'.

The right path through room E is 16 frames slower than the left path. However, this is easily compensated by the three potions on the way.

Room F

https://vimeo.com/811727431

Throwing a potion from the position in the linked video will ensure the potion scare stays in the lower left corner (most positions around this spot seem to work for keeping the potion scare on the left side).
The two first art pieces' health (starting at 4) should be decimated by quite a bit from the hammer and the potion scare. However, using a second potion might also be considered. Throwing a potion to the left from the position in the following screenshot will ensure the second potion scare stays on the left side:

By taking an intentional hit against the third art piece and then immediately throw the hammer, it's guaranteed (?) to be destroyed before Beetlejuice reaches the second door. Just throwing the hammer without taking a hit might still work, but definitely not always.

Level 3-3 (Attic, part I)

Room 0x10-0x12

https://vimeo.com/811727498

The right path in room 0x11 is 80 frames (1.3s) faster than the left path. However, Beetlejuice will quite often take a hit along the right path, even when using a potion. The left path is much safer since it only has one enemy along the way. In case you get to the end of room 0x10 with only one hitpoint left and no enemies to take another damage on, it's worth considering moving on and then take the left path in room 0x11, instead of waiting for an enemy to appear in room 0x10.
The relative x-pixel Beetlejuice enters a portal on will also be the one he exits on, so move diagonally (and not just vertically) to adjust to the most favorable x-position.
If you're one potion short, the one below the fly swatter is the least "off-route" of the ones not collected in the route shown on this page.

Room 0x13-0x17

https://vimeo.com/811727530
Room 0x13 is one of the most critical rooms in a speedrun. There is no known method for consistently clearing the room of flies quickly. Most of the time, it will end up with one or two flies circling around the room out of reach for the hammer and Beetlejuice. Taking advantage of the flies' movement mechanics can however improve the success rate.

The strategy shown here consists of first throwing the hammer horizontally and hopefully take out one or more flies. Collect the hammer when it returns and throw it vertically on the right side instead. When the hammer is off-screen, it will not hit any flies, so it's better to keep it on screen all the time by letting it bounce vertically. The strategy is then to walk around in a square/rectangle to avoid the door and the buzzsaw.
Since this is such a random room, it's actually good to get hit by the flies. Both because it decimates their numbers, but also because it gives an opportunity to "drag" the screen with the remaining flies and align them with the hammer (see how the last fly was hit).
It's important not to get hit by the buzzsaw, both because it can lead to additional deaths, but also because Beetlejuice's will not be able to collide with any flies during the invincibility period.
The outcome of room 0x14 as shown in the linked video is a common one. The potion scare will often prevent one hit, but taking a hit in the upper right corner is often unavoidable.

Room 0x18-0x19

https://vimeo.com/811727572
Room 0x18 is another highly random room. While the mouse's movement mechanics are stiff, they're also completely random. The only knowledge that can be used to slightly improve the chances of catching the mouse is that the time between each direction change is the same.

Room 0x1A

https://vimeo.com/811727482

One can expect typically three hits in this room from colliding with flies.
Keep in mind the portal mechanics to adjust the x-position as required (see description for room 0x10).
There is an interesting alternative strat in this room discovered by 'Bassguy'. It consists of re-collecting the swatter in room 0x13 after the last fly is destroyed and then throw it in the long horizontal corridor here in room 0x1A. It will then hit flies that are one screen off, thanks to a (probable) bug in the code of the flies' hit detection. This trick is demonstrated in https://vimeo.com/811727457. If we assume the average number of hits from flies without the swatter is 3 and the average number of times Beetlejuice hits a fly with the swatter strat is 1, the time save in average is ~1.5s. So if re-grabbing the swatter in room 0x13 isn't out of the way, it's worth considering this alternative strat.

Level 3-4 (Graveyard)

Outside, part I

https://vimeo.com/813961282

The inputs are buffered during the cutscene after 3-3, so just hold down any button to skip the map screen on the first possible frame
The big jump after the moving cloud is a 2-frame jump
By holding "up" during the last jump, you will enter the tower door without having to stand in front of it and wait for the screen to scroll up

Tower

https://vimeo.com/811727689

Note the two golden beetles that are skipped by quickly jumping from the middle platform in the beginning before the screen has scrolled enough to activate them
The ideal situation is to get flower invincibility halfway up, on the right side. Most of the enemies and obstacles can then be ignored. One can still unintentionally bounce off a fly, so some care is still needed.

If you don't get flower invincibility, it's still possible to get through the tower relatively easy, but with it will be slower. The following video shows a route using two damage boosts, so it requires entering the tower with full health, https://vimeo.com/811727386.

If Beetlejuice already has one hit point when entering the tower, it's recommended to skip the first damage boost, https://vimeo.com/811727722.

Finally, if Beetlejuice already has two hit points, it will be even more of a time loss (~2s, compared to getting through with invincibility). There is a flower on the left side of the center platforms that can be attempted for a detour of ~1s and therefore be worth attempting. The last section of the tower can then be cleared as shown above with invincibility. A fairly safe route without getting invincibility from any of the flowers is demonstrated in the following video, https://vimeo.com/811727708. It's possible to jump past the scorpions in faster ways, but it will require precise jumping.

Outside, part II

https://vimeo.com/813961231

The shop visible at around 0:28 contains birdman scares. At this point, you're guaranteed to have enough vourchers to buy at least one. This is not required for the route and will lead to a pretty significant time loss (5+s?), but can still be worth keeping in mind for more casual or marathon speedruns. There appears to only be one other shop in this level that has birdman scares. It's located below the shop just mentioned, near the bottom of the level. This one is very out of the way and not recommended for any type of speedrun.
The ideal boss fight is done in 3 jumps/5 attacks (2/4 possible, but essentially TAS-only since it's very risky and requires fairly tight inputs). The scare attacks have longer reach than the boss's magic attack, so this fight should be pretty consistent.
If Beetlejuice already has two hit points at the end of this level, it can lead to minor time losses in the next level (or even 2+s if an unintentional death is taken). As a mitigation, an option is to take another hit at the end of the gravyard while in the birdman suit to reset the hit points. A safe way is to jump over the 3 frogs before the boss and take a hit on the last one (instead of jumping on the clouds above them, as shown in the linked video). If Beetlejuice's position is adjusted so he takes the damage-boost forward, the additional movements lose roughly half a second over not taking damage. A riskier method is to take damage against the boss right after delivering the final hit. This resets Beetlejuice's hit points without any time loss.

Level 4 (Attic, part II)

https://vimeo.com/811729715

Use diagonal movement to set up the x-position before entering portals (see description for room 0x10). This will both save pixels throughout the level, but also help avoid the pursuing door
When exiting the portal to the room with the sweepers, the y-position will always be the same. This can be used to easier control the potion trajectories. The x-position is still a variable, as well as the throw direction. By entering the portal vertically, Beetlejuice will exit it facing down, while he will face left if the portal was entered diagonally (regardless of if it was diagonal left or right). The sweepers can't move past the locked door, so the best case is when the potion scare stays in the lower room. The graph below shows the result of a test of how many potion scare trajectories stay inside the lower room for the different x-positions Beetlejuice can exit the portal on and for the different throwing directions, while keeping the y-position at 0x49.

For reference, this is the leftmost x-position (0xA2) Beetlejuice can exit the portal on:

As can be seen in the graph, most trajectories from down-facing throws stay in the lower room, but not all. However, when facing left, all trajectories stay in the lower room (except for two from the far right side of the portal, which are anyways out of the way and shouldn't be used). Note that Beetlejuice can't exit this portal facing right, but the right throw direction is still interesting to consider. Most of the time, the sweepers will be on the right side of the room, so throwing a potion directly in their direction could have the benefit of reaching them slightly earlier and thereby increase the average number of hits, compared to throwing the potions to the left or down. This throw direction was therefore included in the test, but the results are not very good. Many trajectories leave the lower room, making the right-facing throws less attractive. Maybe a wider search, including different y-values would provide better results?

Assuming the potion scare stays in the same room as the sweepers, there seems to be a roughly 1/4 chance to take out both sweepers in one throw (difficult to estimate theoretically, so based on limited testing). Throwing a second potion is almost guaranteed to take out the sweepers (again, assuming the second one also stays in the lower room with the sweepers). See the potion management section for some additional comments about the available options.
By holding B+Up while inside the portal, Beetlejuice will buffer a potion throw in the direction he exited the portal and then immediately re-enter the portal. However, the potion throw will then be from y-position 0x48 and not 0x49! At least some trajectories from left-facing throws will now leave the lower room, so it's not recommended to buffer both the throw and the re-entering of the portal (at least not without fully testing the different outcomes from throws from the new y-position). Buffering the throw has no downsides though and should therefore be done since it's a free, albeit small, time save.
Before leaving this level, remember to take a look at the number of lives remaining, as it has an impact on the number of death abuses available in the last level. (remaining lives are only shown when in the menu during the last level)

Level 5 (Afterlife)

https://vimeo.com/811730053

If the screen scrolls too much vertically when collecting ticket #4 (the first one collected in the linked video), there is a risk of bumping into the golden beetle next to it on the way to ticket #3. To avoid this risk, one can drop down from the platform below (with the octopus) and then continue right from there. It's slightly slower than immediately moving to the right, but it's better than risking to bump into the golden beetle.
This demonstrates the currently known fastest route in terms of order to collect tickets and death abuses. However, for the last death abuse (to collect ticket #5) to save time, it can't trigger a continue or get any knockbacks against the frogs above the "rail magnet" (?) on the right side. There doesn't appear to currently be a consistent setup for getting past the frogs without taking any hits.
The following video demonstrates grabbing ticket #5 without death abuse, https://vimeo.com/811729807. It's around a second slower than the death abuse route, but becomes about the same if a continue or knockback is included in the death abuse route.
It has been confirmed through code analysis that all tickets need to be collected in order to exit (the game checks that $85 equals 0x3F, corresponding to all tickets collected, or else the door won't open)
The jump to the exit after death abusing for ticket #5 can be buffered by holding down A before respawning