Do not understand your question, Golem? you mean Character Massive Stone Golem?
Anyway, to complete the Damsel Quest, you need wound the Dungeon and do not receive any wound from Dungeon.
But I'm not an expert at all.
Sorry, yes, as Jey points out I mean the Elemental.
Edit: I changed the subject heading so that it will be more helpful to those with the same question.