The petitioner for this hunt is Balzac - he sits in front of the entrance to the rebel headquarters in Lowtown. He'll tell you that they're training on Dalmasca Westersand, but lately they aren't able to because of a strong monster that's prowling there. He asks you to handle him.
About 150 000 HP
Resistant to Libra,
Vulnerable to Fire,
Ring Wyrm can be found in the western part of Dalmasca Westersand (see map above), but only during the sand storm. The enemy has a lot of HP so the fight will be long, but you shouldn't worry, because the enemy himself is pretty weak. You need for this battle the Wyrmfire Shot and the knowledge of using berserk (or a stock of Bacchus's Wine). In this fight use Bash, Balthier and a healer with a long ranged weapon. With mage cast berserk on Bash and Balthier and then just look after their HP levels. Let him attack from time to time when he doesn't have anything better to do.
His attacks are Rake (ordinary attack), Immobilizega (immobilizes everyone in range), Breath - attack everyone in front and may cause Sap (heal this with Regen). Generally the enemy is pretty easy to handle. Just remember to keep distance with the mage to avoid being hit by his attacks.
Bounty: 200 gil, Moon Ring (1647g), Icebrand