Idol's Ghost Side Quest - Persona 2: Innocent Sin Guides
The Idol's Ghost Side Quest begins by learning a rumor from Maniac inside of Shiraishi Ramen (pictured above); you can only learn this rumor after completing the Giga Macho dungeon. Much like with all rumor quests in this game you will have a very small window of opportunity to complete this rumor because once you finish the Aoba Park dungeon you can never return to it.
Once you learn the rumor from the man inside Shiraishi Ramen you'll want to spread it via the detective agency. All you need to do once the rumor is spread is to run around inside of Aoba Park until you encounter Linda (pictured below) and then defeat her. Linda will drop Linda's Bra once you've defeated her which is the item you'll have to return to the Maniac in Shiraishi Ramen for your reward.
Your reward for completing this quest is a Frei Card.