Throughout my experiences with images, GIFs can only save up to 256 colors. Therefore, an image with millions of colors will not look very good when saved as a GIF, compared to if it was saved as a JPG or a PNG.
Fortunately, video game sprites don't have that many colors, so saving them as a GIF wouldn't affect them much.
You could darken the sun area a bit.
You will notice on Rosalinas' face that her skin has the same gradient quality as the sun, but its hardly noticeable because the differences between the 2 shades of skin is only a few notches of darkness between them.
So if you were to use a darker colour for the sun, it should be less noticeable.
EDIT: I just thought it through again and heres another idea:
The suns area is large, so the limited amount of colours you have have spread out, making the difference between the original colour and the blending colour, very obvious. With Rosalinas case this doesn't happen because the gradient area is so small that your eyes merge the colour 'blocks' as i will call them so you dont notice it. I don't know how to fix that.
Other then that, there's nothing you can do about it, as GIFs, as said by Mario and Sonic guy, only support 256 colours.
(Could always remove the sun of course)
Linear Mode
