↔ If the knees are moving, then the shading on the knees should move as well. It looks a bit odd. So does the eyes, but that's because you don't have a nose to indicate breathing deep, so I can't say anything about that. XD Good either way, I can't animate.

I tried my best at sub-pixel movement. I'm not very good with it yet though, considering tis is my first try.

subpixel movement would improve this. The current movement is lacking in subtlety -- it's like, hardly anything moves, then a huge chunk moves at once. That's why it gives the impression of hyperventilating rather than normal breathing.

The outline jumps randomly, especially on the arms

The jaw/head and shoulders need to move with the rest of the body, also 16 colours is abit much for a piece of this size, maybe you could try reducing colours by replacing close variates of the same colour.