Congratulations on finishing the jam! The character design and animation is production quality. Outstanding. The satisfying mechanics and level design allows players to pull off some pretty cool moves that look even cooler thanks to the constant somersaulting. The visual effects were really effective, too.
I am not sure what you intended for the difficulty curve, but as it stands, it spikes on the level with three enemies to kill mid-air. If you want to flatten the curve more, I have some suggestions. I hope you are familiar with fighting game terminology. If not, message me somehow and I will explain the following points.
One way would be to have enemies that do not kill the player on touch to start with, to get players used to the jump arc, attack timing and double jump timing. If they had an infrequent attack instead, players would just have to wait till right after their attack to start chaining jumps.
Another would be to reduce the attack's startup frames and increase its hitbox size. This should make attacking with the correct timing and distance much easier. Right now, the attack has quite a few startup frames and a small hitbox. Players have to time their attacks quite early and place their attacks at just the right distance, which is rather hard without practice. This is why players kill themselves on the enemies so much: they are unfamiliar with the jump arc, attack timing and hitbox, or they expect something else from the arc, startup and hitbox. The hitbox right now is only when the cat is fully extended, and appears to be a straight line. Personally, I would have started active frames once the button is pressed, and would make the hitbox cover a large area in front of the character.
For double jumping, an impact freeze/hitstop would help with timing and feedback, especially if you allow jump input during the impact freeze. Timing the double jump is rather tricky as it stands, and the penalty for mistiming it in some levels is death by spinning saws.
Now for movement and jumping physics. Acceleration/decceleration is a bit low, resulting in the character sliding around a bit. The quirky run animation with his legs frantically shuffling around contributes to that illusion, heh. Perhaps you could experiment with higher acceleration/deceleration values, depending on what you want movement to feel like.
Jumping over an obstacle while directly next to it fails for some reason. I assume this is a bug, not expected behaviour.
Overall, I believe the core idea is really solid. The character design brims with personality, and the gameplay is promising. With some experimentation I truly believe this can be expanded to a full game.