DRAGON QUEST HEROES II

This trophy is titled "Trader's Pet" and it requires you to maximize the capacity of the Monster Medal Holder for your Monster Minions.

In order to unlock this trophy, three Quests need to be completed during the course of the game. The quests are as follows:
006 - Pedal to the Medal 1
007 - Pedal to the Medal 2
008 - Pedal to the Medal 3

Keeping this mostly spoiler free, Pedal to the Medal 3 unlocks near the end of the game, after the Black Manse appears. The Quest Mistress will ask the heroes to gather a Monsterium Ingot from a Hellion in the Fetid Foothills, but the only way to get the item is by defeating it with Monster Minions. To get to the Fetid Foothills, Zoom to the Desert Plateau in the Grand Desert. Once there, turn around and walk into the teleportal to warp to Fetid Foothills. Inside the foothills, make your way inside of the caverns to the Erdrick shaped area. There will be Wight Priests, Overkilling Machines, and Uberkilling Machines. You'll want those minions to take out a Hellion. Deploy them near a Hellion, but make sure you do not attack it or your AI heroes might kill it before the minions. Once the Hellion is defeated, obtain the item and return it to unlock the trophy.

Here is the unlocking image: