In the Phon Coast there are three "shady bangaas". Once you've found them go up to the bangaa up top behind the "shady bangaas". He'll tell you to got hunt a trophy game, I forget his name, but the bangaa will tell you. He'll also tell you how to flush it out of hiding. Follow his instructions, and you'll be fighting that rare game in no time.

Dispel the game first before charging in to kill him. Buff up your main attacker with Haste, Berserk, and Bravery and leave him alone. when he gets low on health, use a Curaga spell on him. With this tactic, the rare game will fall easily.

After defeating the game, you'll receive a key item called a "Shelled Trophy". Bring that to the bangaa. CONGRATULATIONS! you've now unlocked all trophy hunt. (it's Under Rare Game in the bestiary).