Not an animation edit, but I did a quick palette edit for you instead (with a few small changes to the shading - you had so many colors on the head; you can get away with using far fewer!)
First edit:
Second edit: (shaded the outline, but maybe it makes the ridges in his head look too deep by comparison? Also changed the hue of the shadows on his head a bit.)
First, I picked a slightly less saturated color for his skin; it was a bit bright for me. If you think a color looks good with full saturation, try a slightly less saturated version too, to see how you like it. Very saturated colors can burn your eyes easily, so be careful with them. Next, I changed the hue a bit towards green, just out of personal taste. Then I hue-shifted the shadows towards blue a bit with his skin, and a bit towards purple for his cloak. Changing the hue of highlights or shadows is an easy trick that will usually make your sprites more interesting looking, and usually more realistic looking; there aren't too many scenes in real life where there will be only one light source, so the shadowed areas will take on the color of the second light source.
Also changed the shape of the shading below the collar a bit to try to get rid of the banding a little. I don't know how well I did, though. The shape I picked probably isn't ideal, either.
Softened the ridges on his head by using the colors already being used in the shadows to fade the ridges back into the head on top. If you can reuse a color, then it's usually a good thing to do so. It'll make your piece look more unified, and easier to edit. You can always add more colors later if you decide you need them.
And be careful with the tail; it's shrinking! Make sure that all your masses stay the same size when you animate them. eg: If a ball stretches height-wise from falling, make sure it shrinks width-wise.
Dithering can look good, but if you use it, be careful with it. You can easily add texture to things when you don't mean to when you use it.
Aaaaaaanyway. Cool sprite! I just finished reading The Martian Chronicles, so I had fun looking at it and editing it. =)
One more edit:
Just added a pixel of white to his eyes to make them look shiny and alert! Depends on what you want, though, I guess. He's cool being mysterious and airy too, since he's an alien.
