Agree, it has been like that from the beginning, and it is probably intentional. I think you are going for a very girly feet position, like when some girls stand with their toes facing each other to look cute and childish, but they only do that for a few seconds and it makes for an uncomfortably looking idle stance. However, I admit it gives her a lot of character. Hard decision to be taken here.

Ma3vis is on a killing spree, beware, he will mercilessly GBC your things

That is better already, you got the spirit. It could go further or removing yet some more banding, single pixels, and improving contrast between shades, but you got the gist of reducing the amount of closely packed colors.

As you mentioned losing detail, at this size you are better letting go of some detail an keeping it readable, focusing on key features. Gradients of 1 pixel per shade don't help define shapes, they make things look plane and unatural, you don't want that kind of "detail" if it details nothing

I am in hurry but I'll try coming up with an edit that might give you some ideas.

Well, that depends on the engine / software / language you are using to program it. I believe this should be on the general section instead of pixel art critique

Since it is already here, you could improve the sprite quickly by removing the banding on the sword, front arm and front foot. Try to reduce those gradients, use less shades to define their shapes and try to make the arm, swords and feets be made of big clusters of pixels of the same color. While you are at it, t would be nice if you were to reduce the noise in the floor and stair tiles, it hurts legibility, prefer flat surfaces or, again, textures made of big clusters and of low contrast.

As for your question, you can do that before the assets are loaded on the game, or during runtime.

To do it beforehand, go by Curly's explanation using image editors.

To do it automatically on runtime it depends on the engine. If you use game maker, there are a number of assets to do just that, and I recommend Pixelated Pope's pallette shader on the market, it is cheap and effective. If you are using unity or another engine the solution is likely a corresponding shader that does the same, give google a go.

If I remember it right, in Tic-80 you only have 16 colors but you can choose whatever colors you want with RGB sliders right? I think I actually had some Tic-80 sprites but wasn't able to export them.

I wonder if Tic-80 is related to or a fork of Pico-8, or if they are just similar in scope and aesthetics.