Play it. Really cool so far! Please continue :)
.
.
SPOILER PLEASE DON'T OPEN UNLESS YOU BEAT THE GAME.
.
.
Puzzle island is skippable by doing this jump (see image). Bullet shows from where you need to jump. You need to use coyote time and charged attack for it (clearly i didn't look for ways to skip puzzle instead of thinking :).
Unless you're planning to make another, "harder" version of eye bossfight I think you should make it harder, like make eye way more active. Currently you just spam attack...
Gun seemed useless to me, because you waste shots very quickly. I think it would be more useful if it had about 15 shots by default (+3 per upgrade), and collecting bullets would refill all the ammo.