Not much is known about the Monster Hunter since he only appeared briefly at the end of the episode "No Substitute For Crazy!", he only stated that he was there to hunt monsters and its not known if he is even qualified as a teacher, and knowing the school's prior substitute, its likely he is not.
After Timmy Turner managed to get rid of Ms. Sunshine / Ms. Doombringer by bringing Mr. Crocker back, the former soon got in another accident after jumping into a light fixture while screaming about Fairy Godparents. Shortly after, Principal Waxelplax walked in and introduced this guy, who said he was a "Monster Hunter", to which Timmy replied "There aren't any monsters-" before noticing the innocently whistling Dracula/Frankenstein/Mummy look-a-like kids behind him. Timmy then said to them "You're gonna want to get out through the cave" as the episode ended.