Ed-0: Zombie Uprising

You don't have to complete any dungeon, just start it with the Sumo at least 10 times. You unlock Sumo after beating 3rd dungeon, however if you want to get him immediately go to the temple (it's the building north, 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, don't collect any upgrades, just go through the Tori gate and find nearest enemy. Let them kill you. Repeat 10 times. Done.