Ed-0: Zombie Uprising

You don't have to complete any dungeon, just start it with the Ninja at least 10 times. You unlock Ninja after beating 5th or 7th dungeon, however if you want to get her immediately go to the temple (it's the building north in the village hub, up on a hill) and jump 10-15 times right in front of the closed door. Both locked classes (Sumo and Ninja) will become available.

Again, no dungeons must be completed, only started (including tutorial). To get this ASAP. start "Incident" (first mission) on HELL difficulty, don't collect any upgrades, just go through the Tori gate and find nearest enemy. Let them kill you. Repeat 10 times. Done.