I can help a little.
I think frame 1 and 10 are the weakest right now. That could be remedied by copying frame 5 to 10 and frame 6 to 1 and then perform the appropriate switching of limbs.
Frames 5 and 10 should hit the ground. Animations look best if you take care of the contact points.
Frame 3 and 8 should barely leave the ground, you could even make these frames have contact to the ground, just remember to lower the 4 and 9 frames accordingly.
If you look at your head, it kind of moves in a twitchy circle, however the character is not leading forward in his step (well perhaps a little in frame 1 and 6 but in that case just a pixel) so the head should just move up and down.
It's easier to see if the head has a uniform shape. What I usually do is paint each limb a color of it's own and look at one limb at a time.
Here's a super fast edit:
Next up would be arms, try coloring one arm red and tweak it into smoothness