I did an edit:
yours -> mine

Step one was to reduce the colors. Yours had over 100 colors. Mine has eight. Seven for Pikachu and one background color. I'd suggest using a pixelling program like aesprite, graphics gale, proMotion or something similar. These have indexed color palettes which allow you to keep control over how many colors you're using.
After I reduced the colors I went in and redefined the lighting using the light source from the left and slightly above. Your image also seemed to have light coming from the bottom, so I got rid of that. Having really well-defined shadow shapes will make your images feel nice and solid.
From there I just went in and used the available colors to redraw the outlines and do a wee bit of AA here and there. With a few more colors you could smooth out all the little jaggies and such. I didn't want to redraw your entire shape or anything, so the outline is more or less the same, but I made some alterations to the ears and butt area and cleaned up a few issues with irregular outlines. I like 'em to be nice and smooth if at all possible.
The biggest change is probably the mouth shape, which I redrew to make him a little more happy, and I gave him some eyebrow ridges.
Lighting is probably the biggest factor in the edit, as well as contrast. Don't be afraid of your shadow shapes. I could have pushed the contrast more, in fact. Shadows define form, and if there's no contrast to the light and the shadows the image won't feel solid.
Keep pushin those pixels, man. Practice, practice and more practice.