This is why slow patient consideration is required when dealing with small screws.
Drilling out might be your only option. BUUUUTTTT.
However there are other options if you don't wish to damage it.
Such as soldering/gluing a Allen key into the damaged hole.
Or placing a small bit of rubber into the hole before attempting to unscrew it.
Tapping only works when the surrounding of the screw is stronger then the screw, If the screw is in plastic and you drill, be prepared for damage to occur to the surrounding area.
I would suggest you try a small diamiter screw extractor before trying to drill and tap.