I made it through the first 20 floors solo as a drk hit lvl and got something around 14 points in arm and armor, but been having trouble getting to the 30th floor.

that being said i dont think its impossible to solo, its just your gonna need to be lucky with the chests you get on each floor since you'll be needing to brush through a few floors rather quick while making sure you level up a good amount per floor.

another thing thats important in deciding whether a class can solo the place is healing, which most classes likely wont be capable of with just potions alone 22 sec between each potion use is tough to work with afterall.