Puffy is in Tatroi in front of the Inn and has a text-based game you can play for 600 fol. There are a number of items she may ask you for, but for the trophy's sake the most important one is the nuclear bomb you get from the machinist creation skill.
Machinist kits can be bought in Ionis, the second town in the Van kingdom. You'll need the nimble fingers talent to make anything with them, and nuclear bombs are one of the rarer outcomes, so make sure to save and reload to save money. If nobody has nimble fingers, just pick whomever you can max machinist out with and keep doing it until they unlock a hidden talent.
You may also want to have a flare bomb that can be bought in shops, and a will potion. Will potions can be stolen from Ashlay or Cyuss when you first encounter them, or you can get them out of a Goodie Box that you create with clay using the art skill.
Anyway, the Puffy minigame game proceeds somewhat randomly from what I can tell, but if you get to the point where you meet the archfiend, pick to use an item and pick the nuclear bomb. The trophy will unlock when you do.