As usual, your character design is great. For the run cycle, there should be some up and down motion on her head and torso to suggest weight. (Consult Animator's Survival Kit for a thorough discussion.)
actually, the hair is a good guide to the up/down that's missing - the head should go down when it flaps open and up when it closes...
I think there's something not quite right with the perspective of the legs though - they are quite straight which makes it look like she has no torso and the knees don't look like they're bending... i think they also look like they are moving outwards away from the pelvis and away from eachother at the far pose which doesn't feel natural to me.
Having looked at this again - I think it might also make sense to counter-tilt the shoulders with the legs... don't be disheartened it's just hard to notice all these things until later in the process