I think you're using way too many colors, and it's not just in this piece, you do actually do it a lot.
If you can't shade and properly show form and volume using only 2 or 3 colors, then doing it with more will certainly not help you. Try shading using only 3 colors per element, it should be less of a hassle using less colors, would look more pixel-arty, clear and readable, and would allow us to help you more, as we can identify your problem areas easier.
Hopefully that'll get rid of some of the banding as well. Honestly, the way you're using the extra colors just seem to succeed in lowering the quality of the image.
Make sure you have clean lines, and readable / identifiable shapes.
Also, what adcrusher and LoTekK said.