For the walk, the footwork need to be a little mor evenly-paced. It looks now like the extensions (back and forward) are a little close frame-to-frame, so it gets a stuck feeling. On an animation this short, you want at least 1 frame per step where it's lacking a foot prominently forward or back so that the two feet don't blend into each other). Given the size of the sprite and the frame count, you might wanna implify the walk, too. I can see where you're trying to bend the knees and curl the feet, etc. but it might read better if this guy just sweeps his feet back and forth.
On the jump, you need to do something with his body. When he compresses before the jump, lower his head, tilt the gun down, and then when he jumps do the opposite. This'll make it a lot more natural.
- Adam