Taking an entire section of the creature and moving it upward doesn't make for a very good idle animation xP Where is that motion coming from, how is it possible? Think about how the motion is produced when you animate. In this case, the legs should probably be creating the up/down motion, so they should be animated, and the torso/head would move up/down as the legs straighten/bend.
Could be a breathing animation.
I get what you're getting at though. It's a little too simple of a fix.
Still, IF it is a breathing animation, you might make it so the head doesn't squish. The eyes look fine squinting, but maybe just the head could be fixed. That tail animation is really nice though! Either way, good job and keep the cool animations coming!