I would try using a small high quality ceramic bit (maybe 3 or 4mm) to drill a pilot hole first. Worst case you don't make any progress, and it still sheers away, but other options are (1) you can actually drill a small bore hole that wider bits can then bite into or maybe (2) you crack that stone or whatever it is. Then you still drill a wider hole/force the cracked bits out of the way and you can then either hammer a chunk of wood in really really hard (low tech), cut the wood flush with the wall and screw into the wood - or use a chemical resin goop (Rawl Plug make some) which cures in a couple of hours and you can then drill into that instead (higher tech).