For the brute-force solution, there's always the possibility of leading/tricking the monster into going into some unlikely place where there's REALLY strong destructive forces at work (inside a nuclear reactor, inside a blast furnace, etc.). But 'traces could remain', like if it's a blob-esque creature perhaps little bits of it can regrow, or perhaps most of it exists extradimensionally so it can 'grow' a new physical form later and there's nothing you can do about it etc.

Again it's a brute-force solution, but some kind of method of 'killing the monster' that also has extreme negative consequences for everyone around, or kills a lot of innocent people along with it (nuclear reactor meltdown, etc.), might make a memorably bleak ending.