I modified the leg and arm based on feedback here. Thanks everyone! Let me know if there's anything else that looks out of place.
That makes sense! Thinking about it more, moving it from side to side would use a lot of energy.
The reason I brought up the rotation was because it looks like the hand is moving from side to side, because it gains/loses the highlight on it. If it's going far back enough behind her back to lose the highlight, the pole would have to rotate. If that wasn't your intent, then I think keeping the highlighting constant would help "sell" that she's keeping her hand orientation fixed, and therefore that the glaive also keeps its orientation.
You're right about the readability issues with the highlights, though I don't entirely agree with adding more animation to the glaive. Just think about how a pole vaulter runs with his/her pole. The shoulders of the athlete will sway or rotate a little while running, but the tip of the pole does not move side to side. It just simply moves forward and backward a little. I've done pole vaulting for a couple of years, so I know things about running with a big stick. xD
The legs are hard to tell apart, so it looks almost like the character is moving the same leg with each step, and often looks like the back arm is moving in sync with the back leg intead of opposite it, even though upon frame-by-frame inspection I can tell that it's correct. A common way to set the legs apart is to not have highlights on the back leg and on the upper back arm.
Aside from that readability issue, the animation looks good, very smooth, everything's moving - except the glaive. It's moving forward and back with her arm, but it should also be moving side to side a little bit as her body rotates. Having it foreshorten in a few of the frames (as the tip faces inward) should do the trick, without a hellish amount of work.
I just noticed that the left arm overlaps the glaive when it moves backward . The glaive should always be overlaping the left arm as it's in front.
You might want to save an extra copy before editing, just in case you wanted the sprite to carry different weapons. Good job with the edits, it's looking better.