I think there's confusion about the movement here.  When skipping, you raise one knee passively, and hop with the lowered foot - a complete motion - before thrusting the raised leg down into contact with the ground for a strong second jump/step.  Here, your main force is the exact opposite - it's in the lifting of the leg, which should be relaxed.

They mostly have an issue with the pelvis and hip joints.  Study this carefully, and most of the other issues will come into focus .

Suprised no one has posted this yet   It's a commonly used animation reference around pixelation  

I like to think it's because people have recognized that the top example is static, sloshy and weightless (with a few "catches" too, when the elbows go back mostly) and the bottom run is some jerky monty-python-meets-adam-sandler skit where the guy walks funny while punching himself in the face.  Not a total failure for an animation but absolutely not the sort of thing we should study as an exemple.

While I suspect that 1Up has his own answer, I can say for myself that taking away the pixelliness of a piece has all to do with 2 things : learning by eye, and never banding.  Banding and jaggies (two parts of the same problem - banding is just jaggies over multiple colors) are the single largest giveaways to pixel art.  How work work shadows around and over outlines and how to bleed over highlights to create the idea of an emergent (not delineated) form is something you learn with time and practice.