I'm a big fan of your art style. I'm also going to bring up the jumping as it seems everyone else did as well. It feels like the character has a bunch of balloons tied around him when he jumps, especially with the long jumps. Here's a short list of other things I noticed while I was playing:
(played through twice, died on level 3 to the bats both times)
-Perhaps increasing the speed the character falls to be 1.5ish times faster than it is now, I think it would feel a bit more natural. -The death mechanic is a bit too harsh for my tastes, I feel like if I have a pool of 3 health, I shouldn't die and get reset to the start of the map once I get hit. I should just lose some health and then get reset when I die. (which may have been your intention, but it kinda bugged me a bit while I was playing)
-The bats are waaaaay too broken. The fact that they can start chasing you before you even see them really sets you up for failure, especially when they're coming at you from multiple directions and you only have the ability to really dodge one of them. Perhaps slowing them down or not letting them notice the player until they're illuminated by the light could go quite a long way in making the level feel a bit less unbalanced.
And here are a couple little suggestions I thought of while playing:
-It would be cool if there were hearts or something that you could find in somewhat difficult to reach areas that would restore or even add an extra heart to your health.
-The shield item that you get in level 2 would be cool as a permanent upgrade for your character. Perhaps it could just bump an enemy off it and make them walk in the opposite direction and then have a cooldown before you could use it again. I dunno... just a suggestion. I think it would be cool if you could do something like that and then bump an enemy off your shield to make it walk over a switch or some other similar puzzle.
All in all, I'm interested in seeing what you have planned for this project. I'll definitely keep my eye on it!