Wow! That art! I've only completed level 1 in the web version so far, but I will be coming back to the game. My only complaints are in how the character feels. There's no jump height control. You can't run straight off a ledge. The players controls only register when the animations are complete. It makes the character feel very rigid, contrary to the fluid character. My suggestions are make the character very slightly slippy, add acceleration rather than starting walking / running instantly, allow jump height and wall jump height control, allow the player to exit ledge grab in the middle of the animation, facilitate run while on the ceiling passageways, make the player able to run off a platform, add "coyote time" and maybe make that stepping through gate animation shorter. I know this is a lot, but if you need help I have a basic running and jumping controller for Unity. Still, this is looking like a great game! Good luck!
[EDIT]: I realised there is jump height control. Whoops.