Find the Rat Matriarch west of town and kill her. She will be larger and tougher than the other rats. If you need help, use /map to locate her on the map overview. After killing the rat, return to Lieutenant Cantren to complete the quest.
Every year I'd swear the rat problem around here gets worse, *name*. It's time someone showed those vermin who's boss! I've seen one recently, looked about twice the size of a normal rat. That must be the nest mother. Find her and end her disgusting existence.
Arg! You're covered in rat pieces! None the less a job well done I'd imagine. Good work!