i don't know if I'm saying this right, but on the first animation, it looks like the center of mass is changing rapidly when he hops up don't worry about the character moving off the screen. if it happens, then you get to be lazy. i am 100% not saying that laziness is good. it's actually bad. if you want to keep him on the screen, shift EVERY frame. i recommend by 7 pixels. have fun!
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Well, on my opinion you have to make best poses and try to make more easing and spacing, you have a good anticipation on all punches and kicks. I recomend for you this Tutorial
A lot of explaining but I decided to practice exactly how Senzo animated the wobbly Head bang effect by reanimating it Btw it gave my animating skills a boost so there it is https://imgur.com/gallery/3FsrC