Is the end of the screw exposed? Or is it in a blind hole? If it is exposed, try drilling it with a drill bit from the back side. The bit should bite and turn it out of the hole. If it is a blind hole, you are going to have to get a thin cutoff wheel and grind a slot in it for a flat screwdriver.
If she's really dug in there, and all the other options don't work, you will have no other choice, than to call in an airstrike. I know it sounds extreme, but sometimes it's the only thing that will work.