DeathByJaguar's Pixelart

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Your palette has a lot of room for improvement. The biggest fix you can do is getting more constrast in your shades. The yellows of the hair are too close, e.g. the darkest shade isn't very dark compared to the lightest shade, so you end up with little depth in the shading. The other thing that can improve the palette is using hue shifting, that is making the shades move closer to a different color as you get darker. A common color to shift yellow to, as an example, is orange. Here's a quick edit to show how to apply it. (Left: adding more contrast, Right: adding hue shifting towards orange.)


To save colors, you can share shades between colors that are next to each other on the hue spectrum. In this case, the hair's yellow and the skin tone fall in a relatively close band (orange-yellow), so you can try using the same color for some of the shades for both.