The Trophy Shop is a very rare Mystery Room that appears on floors 91-99 of the Item World.
When you enter, there will be a Thief ("Trophy Shop" class) standing there, just like the common one that gives you a Mr. Gency Exit. Just talk to her, and the trophy will pop. They call it a "shop", but you don't actually buy anything.
If you're having trouble getting this room to appear, simply leave the Item World after clearing floor 90, save, and play through levels 91-99, quit, and reload until you find a Mystery Room gate that takes you there.
I recommend waiting until you're hunting for the 10 Gents/Baal/Prinny Pirates in floors 92-99 in the Land of Carnage Item World to attempt this.