Finally, we have found the fiend who has been stealing our babanas! It is most frightfully fleet of foot, so do not let it escape!
This bounty is available to complete after defeating Rusty's Nightmare.
To find the Adamantiger, head due east of Al Mamoon, as depicted by the blue dot on the World Map.
During the battle, keep control of Oliver; the Adamantiger's physical attacks do MAJOR damage, and can easily wipe you out in three hits. He's almost as hard as a boss, so stay on your toes. Keep your distance from the beast while casting Pulse repeatedly. As for Esther, she will most likely get wiped out by the Adamantiger fairly quickly, so if you can, take a quick break from attacking whenever you start seeing her HP drop sharply. Just make sure to play it both safe and smart.
Defeat it and you'll complete the bounty hunt, return to the Swift Solutions to claim your reward.