General Movement

Spin Dash

When you are standing still, press and hold the D-pad down, then tap A once or twice. Release the D-pad to blast off in a burst of speed. Two tap spindashes are faster than one tap, though there are instances where one tap dashes can be useful. Amy cannot spindash.

Quickstop

Generally, when you land while moving horizontally, you'll maintain some of that momentum on the ground and slide. If you hold down, your character will roll. You generally want to come to a complete stop before attempting to spin dash, which can be done by either using a character's attack, or pulling back.

Slope Jump

When floors are not level, the incline affects the angle and speed of your jumps. When jumping off an uphill incline, the character will go much higher but not as horizontally far. When jumping off a downhill incline, the character will not gain much height, but will gain much distance (and sometimes horizontal speed).

Loop Jump

A variation on the Slope Jump, which takes place inside a loop. If you enter a loop from the left and jump from its top left, you catch the next corner of the loop and are propelled off, gathering more momentum than usual. You get the same effect if you jump from the top right of a loop after entering it from the right.

Aerial Speed

Generally, your character's horizontal speed will decrease whenever the vertical speed is upward, but it will increase when the vertical speed is downward. This means your character will slow down when ascending in jumps, and speed up upon descending. This is also why downhill slope jumps are important for gaining speed, since your character gains no height (thus no speed loss) but will gain speed thanks to jumping downward. Understanding this mechanic is important in gaining speed or losing minimal speed.

Sonic

Sonic is the fastest-moving character all around, but at the cost of not really having any abilities to enhance his movement outside of air dash. This means he can't access spome shortcuts that basically everyone else can access. This makes him clear stages more slowly than Tails and Knuckles, and roughly even with Amy. If you want to play as Sonic, be prepared to mash the d-pad a lot to do air dashes as that's the main reason to use him instead of other characters.

Slide Attack

Press B once to spin slowly. A second time makes him flip. A third time makes him slide. This move is primarily useful for bringing Sonic to a complete stop so you can spindash without accidentally rolling around, though if you want to do this, just press B twice instead of three times. The full combo can be useful for bosses though. The initial roll upon pressing B once can also be useful as he will always roll at the same slow speed, at that same distance.

Air Dash

Double tap right or left after jumping in the air to do an air dash. Alternatively, press a direction while running, jump, then press the same direction again to do an air dash. As long as the second tap is in the air, and not too long after the first tap, the jump can be before or in between the taps. This ability is what sets sonic apart from the other characters and helps him move very quickly, since it gives him more forward momentum each time he does an air dash. You want to do air dashes, especially from downhill slope jumps (and not uphill) since you'll gain more speed that way. It's also useful for adjusting your jumps or if you need a little bit of extra distance from a jump.

Insta-Shield

After jumping in the air, press A again to perform insta-shield. This gives you a very brief moment of invincibility, which can be useful for damaging bosses (particularly the angel island boss). It also gives you an extra bounce if you bounce off of an enemy or item box.

Tails

Tails has the unique ability to fly, which is handy in basically every level. He's the most versatile in terms of aerial movement, but his flight is also very slow. Understanding how to maintain speed from his flight, and taking advantage of slope jumps to avoid his slow vertical flight is key to getting fast times with him.

Tail Swipe

Press B to perform a tail swipe. This move is primarily useful for bringing Tails to a complete stop so you can spindash without accidentally rolling around. It's also useful for bosses, since it has long reach and Tails won't get hurt if you hit something with his tail.

Flight

Press A after jumping to start flying. Each tap of A will increase his height. His flight is pretty slow for vertical movement, but his horizontal speed carries into the flight. It's primarily useful for crossing larger gaps without losing much speed, though if it allows for shortcuts, it's also useful for that. Note that Tails loses speed when flying if he's ascending, and gains speed when descending. So generally, each tap of A will make him lose a little bit of horizontal speed, whereas he'll gain speed whenever you don't, so mashing A is generally a bad idea for horizontal distance. Learn to pad out your A presses so you have exactly enough height to reach your destination while losing as little speed as possible.

Knuckles

Punch Combo

Press B three times to perform a triple punch combo. This move is primarily useful for bringing Knuckles to a complete stop so you can spindash without accidentally rolling around, though only the first punch is necessary for this. He has the best ability for this since his first punch is very quick and shorter than Sonic's and Tail's ground attacks. His first punch also gives him a brief increase in speed before coming to a stop; use this punch to move very short distances very quickly, or off a ledge so he gains horizontal speed.

Gliding

Press A after jumping to start gliding, and hold A to continue gliding. This is useful for gaining extra horizontal distance. This will also always set your horizontal speed to a set amount, so it's useful for controlling your speed, especially if you want to abruptly change directions in the air while jumping. Another nice use is that Knuckles will always be at a complete stop upon landing from gliding, allowing you to spindash immediately. So if Knuckles needs to spindash immediately from a jump, glide just before landing so he doesn't have to adjust his speed.

Climbing

Glide into a wall to have Knuckles cling to it. Press up or down to climb. Climbing should be avoided since it's very slow, though it has its situational uses.

Amy

Amy is the slowest moving character as she cannot spindash nor enter ball mode at will. However, she compensates for having a lot of abilities to control her height and speed, as well as an overpowered hammer. She jumps the highest out of the four characters, even without using hammer flip. Hitting a vertical or diagonal spring (not horizontal) with her hammer launches her much farther than hitting it without a hammer, allowing for several nice shortcuts. Her hammer's hitbox is way bigger than the game makes it look. She's also easily the best boss slayer all around in the game, requiring very minimal luck for some key bosses thanks to how many options she has with her high jump and huge hammer. She's also the only character who can crouch while running, as the other characters will roll instead.

Giant Step

Press Down+A while on the ground to perform a giant step. This is Amy's primary method of acceleration. While significantly slower than spindashing, this is something she can do multiple times without revving nor without worrying about having to come to a complete stop to perform it. Avoid giant stepping into an uphill slope though, since Amy will usually come to a complete halt if done so.

Faceplant

Press B while doing a Giant Step to have Amy faceplant on the ground. Why this is an attack, I don't know, but it does damage bosses and enemies. It's also useful for a skip in Angel Island 1, and going through item boxes that she can't jump around.

Hammer Combo

Press B twice to perform a hammer combo. This can be used to hit bosses with its huge hitbox, and also hit springs. The second hit is sort of not very useful.

Air Hammer

Press B after jumping to have Amy swing her hammer. This is VERY useful as it does not slow her down in the air, and allows her to hit springs while in the air without actually touching them. It's also useful for bosses thanks to its ridiculous reach. Using this on enemies or item boxes will let her "bounce" off of it like other characters do. Keep in mind she can't perform any other air actions after this, until she lands.

Hammer Jump

Press Down+B on the ground to perform a really high jump. Slope jump mechanics apply to this. This ability is very useful as it does not significantly slow Amy down (and can speed her up, if used downhill), yet still has really high vertical reach. Use this to reach higher platforms as necessary. Keep in mind that she cannot perform any air actions from a Hammer Jump.

Hammer Twirl

Press Down+B in the air to have Amy twirl her hammer. This ability is very useful as it sets her horizontal speed to 0 without affecting her vertical speed, no matter how fast or slow Amy is moving. The hammer also has nice horizontal reach, so she can hit springs with this. It's incredibly useful for coming to a complete stop, or basically turning any diagonal spring into a vertical one. This is also what allows her to bounce on bosses to deal damage repeatedly.