"Any monster" means "any monster."
Defeating Monsters with Items and Spells (revised rules, p. 17):
Some items or spells instruct the player to defeat a
monster. When using such an item or casting such a
spell, the player chooses any monster in play and flips
its marker facedown, ignoring all of its tasks.
If the monster marker is in a partial monster task, the
uncovered task requirements must still be satisfied in
order to resolve the adventure.
After either resolving or failing the adventure, the
player collects the defeated monster marker at the
end of his Resolution phase.
Despite the clarity of the first paragraph here, the second and third confuse the issue again, since they seem to assume that the defeated monster is in the adventure pending immediate resolution. I think the answer is that those two paragraphs provide the procedure IF you are trying to complete the adventure where the monster is found. Otherwise, you just claim the trophy.