Move to the left edge of the screen. Oni will come up to you and walk back and forth. Every time Oni punches you, kick him in the face. It will look like he will win, but as long as you kick him every time he punches, you will beat him. (Be careful. If you miss a kick, you will not beat him.) If he punches, but is not close enough to hit you, do not kick. Only kick after he hits you.
Stand still and let Oni move back and forth at you. The third time he approaches, he will throw a punch. Back up to avoid being hit. As soon as he misses, move in and punch his mask once.