Cinderbrick Fort is a long but simple level with a Core; Other than sometimes uncooperative ground, there is not much to it in a speedrun, except in NG+ categories, where a good part of it can be skipped.

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Cinderbrick Fort, New Game

Overview

At the start of the level, wait for the 3 gates to open. Roll past all of the enemies until you reach a switch, and a cage. Use the switch, clean out the obstacles to the right of the cage while you wait for it to rise, and pick up the Scrap Musket. This weapon saves quite a lot of time in later levels.

NG+ - In these categories, of course, you can ignore the Scrap Musket, since you already have it. Two would be an overkill. Also, you're not allowed to have two.

Keep moving until you reach another gate. Quickly destroy the yellow turret to open it(the gate can be skipped by falling, but that would be slower). In NG, use a stationary Hammer overhand attack and a Musket shot, in NG+ you can use any attack.

Pick up the Core. If you didn't level up here, you can roll around this gate from the right side, before it even opens. This is a really easy to do.

Continue rolling through the rest of the level(this part is pretty long in NG, but there is nothing you will have to know other than go fast and try not to fall).

NG+ - At some point you will execute the two Cinderbrick Fort Pike Vaults to a certain platform that you can't otherwise reach, to skip about half of the level. Watch out to not attempt the first one if you only have one Black Tonic left, as you can softlock the level and have to restart it(you'll be stuck on the empty platform without a way to leave it).

At the end of the level you will reach an arena with a gate preventing you from reaching the Skyway. Naturally, you can clip through it by approaching it from the right side, clearing out the debris, then rolling left and slightly up. This will usually require multiple rolls.

This last gate is, unusually, built from two invisible walls. Sometimes, if your positioning to get the clip was off, you will instead roll inside the gate, unable to reach the Skyway. You can either go back and attempt the clip again or try to fall off, aiming up, from the left side of the stairs, which is a slower way to get through this gate.

NG+ - If you have Black Tonics left, you can do a Pike Vault to try to get over this gate faster than with the roll clip, at about the same spot that you do the normal clip.