What do the import settings for your image look like?
Switch to Import tab and click on your image to show the details.
In case the mode is set to VRAM compressed, set high quality to on.
Or try another mode. Not exactly sure which one is the best for sprites.
Hover over the mode to see a tooltip that explains the pros and cons for each mode.
EDIT: Your second image looks like mine when I have vram compressed and no high quality.
I forgot, after changing the mode, you have to press reimport.