The opponents are both Zelda and Mewtwo. The match starts off with Zelda, and she can be attacked without penalty, but KO'ing her after Mewtwo appears causes the match to end in failure. Mewtwo joins the fight after fifteen seconds - KO'ing him is the goal.
The title and situation of this event is based on the Pokémon movie Mewtwo Strikes Back, where Mewtwo makes Nurse Joy (here represented by Zelda) its mind-controlled servant. This also explains why the player encounters Zelda before Mewtwo.