First world complete in a bit under 8 minutes.
Here Goes Jelly
Uses the balloon clip (due to Exonym) to get rid of the balloon faster while still skipping the hammer blocks. Waiting for the moving platforms can be avoided with a walljump. In fact, the walljump can be done a frame earlier, but the false teeth give a horrible pattern that loses much more than the frame. In the WIP, one of the sets of false teeth despawns offscreen. It is possible for both sets to despawn, as I found with my original (much slower) setup for the walljump, but I think this requires spending more time waiting than it gains (I should check again to be sure)
Marble Alley
Not much to say. Annoyingly, a marble forces us to slow down. Also, due to the short time limit of the stage, collecting more fruits and notes would make the countdown take longer.
Drum Solo
Due to the positioning of the puzzle piece, it is faster to do a non-optimal (1 frame too long) midair jump at the start of the stage. Holding B after rolling off a ledge with the ball allows you to levitate for a short amount of time, which gets us underneath the annoying plane enemy at the end of the stage.
Barmy Army
The first drum bounce is much slower to use at the beginning of the stage because you can't get enough speed to the left in time. It's possible to finish the stage 9 frames faster by finishing in midair, but walking into the enemy sets the flag for a textbox, which would otherwise be carried over into the next level and lose 40 frames.
Blocks Away
I don't have anything to say about this.
Mini Maze
The post-death level needs a note since I don't think you can walljump while mini - your speed is lower so you don't clip into walls as far, and the mini hitbox doesn't seem to have the same asymmetry that makes walljumping work. The death route saves upwards of 6 seconds, so it is very likely that it will save more time than getting a 1-up for it loses. Regardless, the game hexes very well within levels themselves, so it shouldn't be an issue if this needs to be changed.
The Darkroom
We lose 3 frames to get the note off the enemy we kill, as otherwise the lava does a very slow death animation. All of the previous enemies seem to be in unfortunate places to get the note from elsewhere, and the lightbulb cannot attack so we cannot pick it up later. We cannot just get rid of the lightbulb earlier either, since its hitbox makes walljumps much less precise, and so chaining them is a lot faster.
Dolls House
Double walljump :) The turnaround before the second walljump can be improved by 4 pixels, but it also lands significantly later, which forces the second walljump to be from a lower block, losing time overall. It is also possible to die at the end of this level, but this loses time overall due to the extra transition, and finishing the level on the ground saves a lot of time in Bossy.
Bossy
Bossy's pattern is fixed. The hits at the start are made possible by finishing the previous level on the ground so we can jump directly to the helicopter powerup. One shot hits a disc shot by Bossy instead of Bossy itself, but this allows shots from much closer, so more damage is done in the first part of the pattern.
I feel like there was something general I wanted to say but I don't remember what it was.