What bit are you using? Try the JIS equivalent of that bit, and push down HARD. As long as you have the correct sized bit, this has plenty of head(?) to come out.
Screwdriver bit, there are lots of them. JIS (Japanese Industry Standard) screwdriver bits are different from Phillips. They have a shallower angle on their blades, and while a Phillips bit will "fit," it won't seat all the way down into the screw head. When higher torque is required to tighten or loosen the screw, a Phillips screwdriver will strip a JIS screw, and vice versa.
As others have mentioned, carefully drill it out with a teeny tiny drill bit, maybe make use of a teeny tiny easy-out. Replace with a slightly larger screw or just leave it empty.