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Nice! art style is great, both in terms of visuals and audio. Music especially is a standout, I really like the mix. 
gameplay wise, I have a bit of feedback:
Firstly, the platforms are quite frustrating. Most of a playthrough is spent just waiting for the platforms to move. I'd definitely start by reducing the time that they wait in between cycles.
I'd love to see more enemy variety, I reckon if you designed an enemy that was radically different from the enemy you have already that compliments them in some way you could add a lot more depth to your challenges.
(1/..)

Chain jumping on enemies feels great, you could consider adding a combo system that keeps track of the number of enemies destroyed without touching the ground and gives the player some reward for maximising their combo. that could add a lot of depth and replayability as players try to maximise their score. 

Enemy design wise, maybe something like a bullet bill turret that shoots projectiles you can bounce on, this would open up new level design possibilities. 

I'd definitely say the jump feels floaty, that might be what you're going for, but I'd suggest experimenting with a cancellable jump.
My game uses a gravity handler system that changes the player's gravity based on their Y velocity, that plus a jump cancel that reduces the player's Y velocity when they release the space bar after jumping gives you a lot of customisation options for tweaking the jump.

Also just noticed you can press the enter key to go to the next level, that's a nice touch.