CandyFace
That a pretty good start, you've got a lot going on, that's for sure. Be careful not to dither too much though, as it tends to get hard hard to notice the important changes. The jacket fluttering in the wind looks nice and the feather too, but if you zoom out to 1x, then you won't notice all the other fancy sub pixel animation you've added to the beard, the jacket shadows or the skeleton button. Remember to zoom out a lot when you work with your sprite, and make sure you can see the changes, so they're not wasted effort.
Also the head is not the only thing that moves, it's subtle but you'll notice you're actually moving most of the upper body when breathing, try to add that to your character.
Mix between the animations methods, for example.. animate the beard by making subtle adjustments, and move shadows according to that. Move away from the muddy, boring color transition from gray to more gray.. experiment, use blue or purple.. saturate and add some contrast, Pyxel Edit's shading panel can be a very powerful tool for this:
Dithering, a technique often used to color blend instead of adding additional colors to the work, and back in the SEGA saturn days, used a a way to simulate transparency. It can make your work look outstanding if used right, but when used wrong it really convolutes much of the effort you're trying to put into your work. A good rule of thumb is to only use it when you think it is a ABSOLUTE must.
You can read a bit more about it here:
http://pixeljoint.com/forum/forum_posts.asp?TID=11299&PID=139320#139320
These subjects in particular are interesting, if you don't want to read everything ;)
III. Terms to know
IV. Things to avoid
I'm looking forward to seeing your improvements ;)
