Arms and legs seem a little chunky.  A hair idea?
Edit:

@Ambivorous  Thanks for posting the vid.  Nice to see the process and your studies.  Has a classical painting feel to them.

Yeah, too many colors tends to muddy things up.  Sort of less is more with pixel art.  Plus it makes pixeling easier when a limited palette is used, esp when animating, as you can imagine.

For a small simple game, I like it.  The animations are quite nice esp the archer.  Everything seems to fit background wise.  My first though was, the foreground trees could be bigger, but that would get in the way of the animations.  Unless you make the trees into sprites and place them randomly and have some layering going on.
Also, it looks like you have different scaling between the background, hud and the sprites.  Making the background and hud the same scaling as the sprites would look better I think.  In some of the games I make,  I scale everything up except for the fonts, only for better readability.
As with any game dev, it's a matter of how far you want to take it.