This page explains how to start and complete the Fireproof Lizard Roundup side quest.
How to Start the Quest
Talk to Kima at the Southern Mine area of Death Mountain to start the quest. The mine is northwest of Eldin Tower.
How to Complete the Quest
There are many Fireproof Lizards in the Southern Mine area. To make it easier to sneak up on the lizards, be sure to crouch, or you can wear the Stealth Gear if you have it. The Stealth Gear can be purchased in Kakariko Village. (Read Seek Out Impa if you need directions to Kakariko Village.)
After you have collected 10 Fireproof Lizards, give them to Kima to get Flamebreaker Armor. Afterward, Kima can buy Fireproof Lizards from you.