When you are fighting Mynce in the level Teachers and Traitors, keep killing her until you reach the outer area with broken staircases. An easy way to end this fight is to jump into the air (rebound kick for extra distance if necessary). Mynce will jump after you and fall to her death.

Take note that this will NOT kill Rayne if you manage to keep her in the air long enough for Mynce to jump after you. After the cutscene, Rayne will be standing on the bottom platform as she would be if you defeat Mynce the normal way.