You go up in level as you defeat monsters in the game. To get the highest ranking, you must defeat all the monsters. (The rest of the hints are a list of all the creatures you can defeat for experience.)
Wine Cellar: Rat-Ant, Skeleton, Discipline Crab
Moors: Eldritch Vapor, Guttersnipe
Lighthouse: Giant Spider, Giant Slug, Dust Bunnies, Dornbeast
Accardi-by-the-Sea: Monkey Grinder