During Disc 2 when you visit Treno you'll have the option of fighting a monster at the Treno Weapon Shop. You'll have to choose one party member to fight the monster. There are four monsters to fight in Treno total. The first can be fought in Disc 2, the second two can be fought in disc 3, and the fourth during disc 4. You won't receive Exp or AP in these battles but you will receive a prize. The prizes and monsters are as follows:

Also note that if you get KO'd in one of these battles you will not receive a Game Over but you'll use any items you used during the battle.