The arms still look like they're sliding as they always stay on the same line.

I've changed the arms so when they're at the end of the swings the "hands" kind of flit up. You'll notice also that I cut down on the secondary animations like the skirt flowing and the body shifting (which I realize I started that
) mostly because I was so distracted by it that I couldn't figure out what was wrong.
As rikfuzz said the head needs to be up a total of twice, when the feet are in the passing position (the planted leg is fully stretched up and the other leg is passing through the same other leg), so I went ahead and did that.
After that I found that it was odd that the was not moving down when the torso went down, which really didn't make sense, so the skirt moves down as well.
The thing that I think bothered me the most until I figured it out was that both feet were never on the ground at the same time. It's sort of a type of running when you do that.
I also messed with leg positions so that they would move a little smoother. As well, I added the front part of the foot only on the planted foot.
The head jiggling that you did I think would be fine but it's too choppy as it is. I think if you held the head down at the bottom for another frame or two it would be less choppy.
On the hair I added a little bounce. Not really sure if it looks good, but there you go.
I'm incredibly tired so if something doesn't make sense, I apologize. 
Oh, so they can't stay on the same line.I tried changing it before, but I couldn't make it in a good position.
And
now I get it! It's supposed for the entire torso to go down, and not only the head. That's why it was a little strange.

Here it is!
Looks like Miro finished an edit before me, but I made this to further illustrate the point:

Kinda redrew the whole thing, but you can just pay attention to the bobbing and limbs if that's what you want to work on.
Yes! I understand now.
Oh, and one more thing. I didn't explain her clothing very well.
Well, she uses a
white jacket (I didn't know how to make it look like a jacket, so it is all square), and a
orange shirt under her jacket, and a
skirt that is "chess-like", I mean, like, black, white, black, white... I hope you understand me.
And one of her arms is a
cyborg arm (She lost her hand because the spirit of the abbyss removed it from her, so the medics replaced it for a cyborg arm), so it's a little mecha-blue like, and the other is supposed to be the jacket.
Oh, and that on her neck is supposed to be a
scarf. I didn't finish it.
Thank you!