I got to the eighth square directly above the starting one.
There's a sorceress there who has three different instant kill attacks. :(
After that, I did cheat. It appears the enemies level up with you (some more obviously than others, the human enemies all have level numbers in their names), FF8 style. Also, FF8 style, it appears the way to become obscenely powerful is to never pledge gold to get your base stats up, but instead to improve your weapon.
With my NaN gold, and 200 Strength, Vitality and Intelligence I set out to conquer the sorceress, which I did. The next boss, Efreet, was basically invincible.