How do I beat myself after taking the X Potion?

When I use the X Potion from any level, I get teleported to an area where I fight myself. But, I can't seem to win!

Whenever I try to heal, the other me heals as well, so I keep dying before I can kill myself! How can I win?

You can find the answer by reading the scrolling text in the background (use the time slowing ring if you find it hard to read). The answer:

Wear the crown you get from killing the Octopus King and just autoattack. You'll survive on 1HP.

You must obtain the Octopus King's crown by beating him in the cave. Afterwards, you'll have Self Confidence and can kill your doppelganger. Otherwise, you die when your doppelganger dies.