big, giant, huge, large
hideous, horrible, ugly
bug-eyed, hairy
cheap sci-fi movies with bug-eyed monsters

six-eyed, three-headed, etc.
evil, heartless, inhuman
What sort of inhuman monster could do such a thing?

alien, mythical, prehistoric
sea

create (often figurative)
The government has created a bureaucratic monster.

battle, defeat, destroy, fight, kill, slay, vanquish (often figurative)
He wanted to fight the monster of poverty.

be inhabited by
a barren wilderness inhabited by monsters

attack sb/sth, devour sb/sth, kill sb/sth
lurk
growl, roar

Monster is used with these nouns:
storm, truck