Pixelfus, my first try!

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When you first start spriting, using false restrictions is not the best way to go. The gameboy can handle a much larger color palette than what you have above.
Your sprites also lack depth, as there currently is no shading involved.

(just an example of color palettes and I just took a few colors from LoZ: four swords)

On the other hand, just because you can use more colours doesn't mean you have to. Your edit uses more shades than needed and the shading is a gradient and thus doesn't show the shape and volume. So all in all, it's not a huge gain.