Esthar Elynoyle Fixed Encounters - FF8 Guide
After completing the Lunatic Pandora dungeon in Esthar you'll be able to return to the city and get into a fixed encounter against an Elynoyle enemy (pictured above and below). In order to initiate the fight against the Elynoyle what you'll want to do is speak to the NPC dressed in black shown in the screenshot above. He'll laugh at you after which you'll be thrown into a random battle against an Elynoyle.
Elynoyles are known for dropping Energy Crystals which can be refined into Pulse Ammo, the most powerful ammo for Irvine. They're also used in multiple Ultimate Weapons, here's a list of them!
Keep in mind that you will have to fight the Elynoyle enemies without using Mug on them, that will make them drop no items and will result in no Energy Crystals for you! You'll also not want to assume that these fights are going to be a piece of cake because there's only a single enemy.