Rogue Galaxy Quarry: The Tower Predator
In order to reach The Tower Predator you'll want to teleport to floor 6 in tower 1. After you do that you'll want to take the elevator up to the seventh floor and from there go to the walkway bridge just like where The Tower Matador is located, The Tower Predator is in an "outside" area on a walkway. Luckily, I have a screenshot for this guy though!
Perfect Elixirs can usually be obtained from boss fights throughout the game and are rare occasional prizes. Hopefully you haven't been using them (you shouldn't have needed any so far) but if you have you'll have to wait until the end of the game to buy more in order to do this quarry.