The rules seem to be contradictory with respect to what happens with monsters who appear in an encounter and get defeated.
From p. 22 of the rulebook, "No matter how the encounter is resolved, the monster is never left on the board. The monster is returned to the monster cup, regardless of whether the investigator evades or defeats the monster, or is knocked unconscious or driven insane by it." To me this suggests that, if you draw an encounter card that says "a monster appears" and you fight and defeat the monster, you don't get its monster trophy (because it goes back to the cup).
But from the very next paragraph (still p. 22): "When a monster but not a gate appears in an encounter, the monster does not stay on the board. If such a monster is defeated, players may take it as a trophy (unless its special ability says otherwise)." To me this suggests that, if you draw an encounter card that says "a monster appears" and you fight and defeat the monster, you do get its monster trophy.
So, do you or don't you get the trophy?
I've always played according to the latter rule (keeping the trophy for any non-Endless monster you kill), and I guess this is also justifiable if you assume that more specific rules override more general rules. (Furthermore, many other bits throughout the rule book make reference to returning these monsters to the cup if you evade them, whereas this one spot on p. 22 is the only place that mentions returning to the cup if you defeat them; so it seems that keeping the trophy is more in keeping with the "spirit" of the rules expressed throughout most of the rulebook.) But I find this whole section rather confusing.