I recently managed to recover one of my old projects and cobbled together a video.
This is just a small obstacle course for testing a bunch of physics nonsense. Stuff like...
...basic movement
...gravity and different height levels
...conveyor belt physics
...special surface physics (ice, honey)
...claw swiping and fire breath
...ground pounding and ground pound jumping
The video framerate is kind of bleh because I have like no experience recording my own screen. The fire doesn't have a sound effect yet, and I want to try adding particles to a bunch of things later.
I've taken a look at the walk cycle animation and I think there needs to be a tween in between frame 3 and 4: the head snaps back into the same position as frame 1 while skipping the frame 2 tween (the same happens at the loop point, between frame 6 and 1).
For the run animation, you might need to introduce height changes like you did with the walk cycle as running follows pretty much the same rules as walking.
I've been kind of dissatisfied with the head motion for the walk cycle and will probably try to fiddle around with that some more in the future. One thing I've considered was some kind of elliptical motion that might make it look a bit more stable.
I do kind of like the run cycle without the height change though.