This trophy is called "Ugly Fellow" and it requires the user to defeat an enemy with the item called "Hyottoko Mask."
Hyottoko Masks are a pudgy faced mask which allows you to spit fire when used.
Enter your Equip menu and equip them to any of the Shortcuts. The easiest enemy to use them on are Skeleton Warriors. Attack them once or twice to reduce their health, use the Hyottoko Mask within close proximity to kill them, and the trophy will unlock.
I earned mine in the Twilight Mission "Foreboding Seas" against Umi-bozu.