Battle arena is an arena in Wild Arms run by Duke Pegucci. You can pay 1000 gella in order to face challenging bosses and win prizes. After each match you win you get the option to continue or to end. Depending on the amount of matches you fight, you'll get different rewards; the longer you stay, the greater the reward.
Round 1: Medea
Round 2: Badnews
Round 3: Javawalk
Round 4: Riversider
Extra: Flash Boomerang (reenter the arena after winning all four rounds, AND have the item "Saber Fang" in your inventory)
Rewards you get after quitting after:
Round 1: 10 Heal Berries, Goat Doll, Lucky Card
Round 2: 1 of each Apple, 5 Potion Berries
Round 3: 3 Secret Signs, 10 Magic Carrots, Ambrosia
Round 4: (if you defeat all opponents): Duplicator, 3 Nectar, Full Libra
Flash Boomerang: Divine Blade
There is also a secret boss in the ancient arena, but outside of the actual arena, Angol Moa. To get to Angol Moa you first need to go to the other side of the arena (the side where Duke Pegucci is sitting), after that up the stairs. Here you should see a blue mirror, if you punch it using the Power Glove it will break and reveal a secret path. Just walk straight forward and open the 5 sealed doors (you'll need 5 duplicators for this) and walk past the stone tablet into the next room. Walk to the edge in the middle and a text will appear "There is a psychic force attacking! Do you want to sit it out?". If you answers "yes" you'll enter a battle with Angol Moa.