Through the entire game.
Mainly in the Caverns of Chaos.
The object of Titanium Man is to finish the game with the lowest level character possible. Finishing the game is defined as follows: You must close the Gate and leave the Drakalor Chain. You are not required to do any side quests. You do not have to rescue the puppy or save Khelevaster or get the Trident or anything. Just complete the game.
Since if this challenge was open to any race, a troll would always win for obvious reasons, so the challenge is relative to different races. I think teleport and teleport control would really help out with skipping through levels quickly. I also wouldn't even bother with Yriggs or the arena or anything but finishing.