Here's a short discussion from Kinnas about the subject:

A boss sprite for a game.
Also a quick lousy edit on the grasshopper boss

Basically I just dragged a few sliders around: desaturated,
added more contrast in levels (should have used curves, the levels made the whole thing too dark, there should be more mid-value areas in there I guess) went over the contrast in curves and saved in gif at 18 colours (though by hand this could be cut down drastically. Which not only is awesome for the skillful application for colours but also makes reading the character easier)
For such a simple colour scheme you had a ridiculous amount of uselessly similar greens which were all blended way too vigorously and didn't go dark enough. This resulted in a very flat look. Ideally I think three shades establish the main shapes, two shades to blend them, and a shade for highlights and a shade for the darkest dark. So for a unicolour beast like this it should take no more than 7 colours. I guess two types of blue would add for a much needed backlight (for variety and whatnot). So that would up the colour count to 9. Maybe a few extra colours for patterns to break the shapes up in interesting ways?
But all that counts only if this silly 'pixel-mastery minimal for maximum' is a goal on its own. If 32 colours is a must then I guess 32 colours is a must but the values are still spaced way too evenly to allow the shapes to read properly.
Here's your version desaturated:

Here's my quick fix:

WARNING TANGENT:It's something I'm taking into account with my current project: the mc has the ability to run really fast, and because I'm working with miniscule 16x16 sprites, I wanted to make sure that the player would be able to keep visual track of the character. What I found out was that the part of the human brain that tracks motion only sees in black and white. So I made the player sprite darker accordingly.
~~THE MORE YOU KNOW~~