Depending on when you visit the Weapons Shop in Treno, you can have one character duel with a monster that the owner has caught and caged under the floor. You can fight one monster during Disc 2, one of two different monsters during Disc 3, and only one monster on Disc 4.

Griffin
Use Steiner and equip the following: Gold Choker, Auto-Potion ability, and Bird Killer ability. If you have five or more Hi-Potions, sell all of your Potions so that your Hi-Potions are used when Auto-Potion kicks in. Make sure Steiner is at least level 7. Use a tent on the monster (see the Catoblepas strategy), and it will receive every status effect that it cannot Guard against.

Catoblepas
Equip the Jelly ability and Beast Killer ability, and use equipment that defends against Thunder and Earth or use the Auto-Float ability. Catoblepas remains in Treno until the end of Disc 3 or until you defeat the monster. Use a Tent on him until the beast bites him (this happens one-third of the time) and he will receive every status effect that he will not GUARD against. You can also use the Blue Magic Roulette if available. Since there is no consequence for losing the battle, use this ability until the happy little finger lands on Catoblepas.

Amdusias
Amdusias casts Lv4 Holy, so avoid levels that are multiples of four or equip equipment that defends against Holy. Equip the Antibody ability, and defend when it's in the air because it will only use physical attacks at this point. Equip Auto-Reflect if possible, because it only uses magic on the ground. Also, equip Auto-Regen or Auto-Potion and the Counter ability if possible. If you have Reflect, Amdusias will kill itself and you can just defend. At this point, use a Tent on the beast until the snake bites him (this happens one-third of the time) and he will receive every status effect that he will not GUARD against.

Behemoth
This monster is extremely difficult, even at high levels. It's best to use an attack that kills the Behemoth instantly. You can use the Blue Magic Roulette or Zidane's Soul Blade attack when he has the Sargatanas weapon equipped. This will instantly petrify him.

The Weapon Shop monsters don't reward you with any EXP or AP, but the store clerk will give you a prize for each monster you defeat