The petitioner on this assignment is Homesick man. He can be found inside the Armaments Shop in Archades.
He wants you to kill a giant Titantoise, which prowls in Sochen Cave Palace and prevents him of getting back home.
The easiest way to get there is through Old Archades or from the Sochen Cave Palace gate crystal. Use the elevator to get down and you'll find the Dark Steel just in the next chamber.
About 115 000 HP
Resistant to Libra,
Vulnerable to Holy
This enemy has a lot of HP (as for his rank), so get ready for a longer fight. He's vulnerable to Holy, but don't use this spell if you have it. The casting last long and it's not worth the damage it deals. You'd better use a weapon with Holy element (e.g. Holy Lance) and cast berserk on the character, which holds it.
Dark Steel uses Power Spin which damages everyone around him and may cause slow, Flatten, a very strong attack aimed against one of your heroes, Stone Gaze which may cause Petrify and Darkra which deals dark elemental damage to everyone in range.
Bounty: 3000 gil, Lead Bolts, Adamantite (1479g).