EDIT:
Everytime I make a long ranting crit like this I'm a bit scared I'll scare the artist away from whatever subject they're attempting...so even though I really shouldnt (JOBZ!) to make up for it I ended up making an edit. That I have animation blue balls from concepting areas for too long (which I had never done before and I'm finding a bit hard) probably has some hand in it too:p
Click to see my gif edit of the transformation part

I did this after writing this bigass post. The post contains many of the ideas I used here, although I do go a bit effect crazy :p but really, until you get timing effects are more of a distraction, focus on that.
The effects went a bit in the gurren lagann/Imaishi style. watch that or something by studio trigger, they're the biggest exponents of anime intensity so try to aim for that
https://www.youtube.com/watch?v=UQrvmNz6STE hell, just try for any style of animation you admire (mitsuo iso is very cool too!) just dont...keep on making movement where limbs move at an evenly spaced rate.
I'm a little bit...shocked that the only "put on uniform while posing exageratedly " action you could think of was ironman...? anime has loads and loads of the stuff, they call it henshin
https://www.youtube.com/watch?v=0HtLiL-uDz8 personal favorite from my childhood. heh, the influence kinda shows
The reason we dont get that she's jumping is not because you dont have room in your canvas to actually move her upwards, the reason is because you made a very halfassed buildup pose for her jump and you also dont leave her jumping long enough to convey that she's in the air and she's moving.
Look at her crouch, she is crouching still with her torso almost completely vertical, you DO NOT see that in anime, their crouching stances are always as extreme as they can be, you cannot do that by keeping most of the pose from the last frame, you need to redraw a lot of it. I'm not really sure at this point, can you draw a head tilted downwards? you need to do that for that pose. Also, this IS something you could benefit from doing in real life, super soldier or not only someone doing a dance or a yoga pose ducks like that, your animation here much like your animation of that fire kick still has that sort of dancey impactless floaty quality to it because you're not being extreme enough with your poses.
Here is a post by pixel pile driver about timing, this is what's missing from your animations to really make them look like out of Hyper Light Drifter.
http://wayofthepixel.net/index.php?topic=14964.msg137576#msg137576Try easing up on all the effects and focus on injecting simple movements with a lot of energy, your animations wont really get better until you do.
http://afraux.tumblr.com/Try looking at one of his gifs and pay attention to how many frames he spends at the beginning of the action and how many he spends at the middle, how many at the end. You'll find it's completely different from what you do, this is why you cannot do what he does by making your animations the way you always did and then tweaking each frame's timing afterwards
in fact, dont tweak the frame's timing at all. just draw the frames while being more mindful of timing. try setting all the frames to 10 (GIFS divide seconds in 1/100) so you KNOW you're doing the timing with the chanes in each frame, not with how long each frame lasts.
What program are you using to animate? I'm starting to think you're not using something that lets you animate as you draw. you need to use onion skin if you have it to see how much each frame is changing compared to the last one, or atleast flip back and forth so you have the best chance possible to improve your sense of timing