Instructions
Complete all the quests for the instructor associated with your character class. For example, Night Walkers must talk to the thief instructor in the Jazz Bar of Kerning City.
Finish the "Rigorous Training" quest, of which there are four. These quests are administered by NPCs close to the instructor and require you to kill local monsters such as the slimes in Ellinia. Lucci in Ellinia offers the quests for magicians while Muirhat deals with pirate training in Nautilus. Talk to your instructor after completing these quests.
Follow the NPC's instructions to complete the series of small quests that unveil the demon plot. For instance, Grendel the Really Old will send mages to Kyrin in Nautilus. She will then ask you to kill ribbon pigs and send you to talk to other NPCs who will require you to collect items. At the end of these quests, return to your instructor to receive the demon embelem that will allow you into the demon's doorway.
Travel to the demon's doorway and enter. The doorway is located in maps just outside the down. The Top of the Tree That Grew to the North of Ellinia houses Marbas, for example. Continue through the portals until you reach the map where the demon exists.
Defeat the demon without dying. Return to your instructor to receive the corresponding demon hat.