The most commonly used formats that can handle semi-transparency (usually called alpha transparency) are .ico formats and PNG
GraphicsGale can work with alpha transparency, try looking it up in the manual. It's also in the menu under Image -> Add/Make/Delete/Invert/Duplicate Alpha Channel
I prefer doing things in photoshop though, so I don't know if GG knows how to properly save alpha channeled PNGs or Icons. I usually don't touch pixel art with photoshop, this one's an exception though, since these more powerful options of GG tend to be more cumbersome than the PS equivalent.