Hey! Look, more time for the forums
I totally love the character design, reads so clear that is scary, I may have to put you down to eliminate the competition
First of all I have to say I've never worked with restrictions in mind so my advice may not be as useful for this specific case but here I go:
- As it is, well, the punch feels weak and the reason is exactly what Cels told you, It's all about those hips baby, my advice when animating anything is to picture yourself as the subject, in this case, throw some punches and try to feel what every part of your body is doing.
- More specific, I think there are two principles of animation that can be applied here without hindering playability: Anticipation and Overshoot. Since this is for a game anticipation can't be actual frames, instead of that use the smear to convey that anticipation, simply draw the smear from his back to the front, this gives the impression of anticipation. As for overshoot, well, in this case is better to add another frame for it and push everything a pixel further, the feel a single frame can provide is out of this world.
- Again, not sure of the palette or the restrictions, but for the idle you may want to try sub pixel animation like in Metroid for the SNES, so, some movement of the outline, followed by movement on the shading only (Pretty much an after image, like Megaman dash)
I'm sure my edit has many improvements that can be implemented to give it a better feeling so if you guys have any ideas I will be really happy to read them! I hope the edit helps with your project!