Doppelganger can be beaten every time with this strategy. All you need is an axe which is one of the easiest weapons to obtain. Win every time. Sometimes he walks or jumps off the edge, just try again. For some reason, I did not see this strategy in any text or video walkthroughs, I stumbled upon it while practicing the fight the "normal" way. Let me know if anyone else has pointed you to this strategy.