Kuchisake-Onna Side Quest - Persona 2: Innocent Sin Guides

The Kuchisake-Onna Side Quest begins by speaking with an Old Man outside of Mt. Iwato in the Rengedai prefecture. You can only start (and complete) this rumor after you finish the Aerospace Museum and before you finish the Mt. Iwato dungeon. As usual in this game, once you finish the dungeon associated with the rumor you'll no longer be able to complete it.

Once you've picked up the rumor via the Old Man and spread it at the Kuzunoha Detective Agency all that's left for you to do is run around Mt. Iwato until you encounter Kuchisake-Onna. If you've gotten into the habit of using Estoma already you'll have to break it for this rumor because Kuchisake-Onna is a level 26 demon which is a much lower level than the rest of the monsters you'll fight here.

Defeating Kuchisake-Onna will get you Kuchisake-Onna's Mask which you'll want to return to the Old Man outside of Mt. Iwato for a Megido Card reward.