As the achievement states you must obtain all keys in the game and use them.The keys are as followed:
Train key (this will be the first one you get)
Conductor office key
Gold and Silver rings for the briefcase
Fire key
The locker key: This one is missable and is found on a box in the room with the waterfall across from the Battle Arena room in the basement.
Water key
Incinerator Key
The two elevator keys obtained when defeated the Leech Queen for the first time.