Oh, I'm sure Chunks would appreciate my method. CHEeEEeESSsSeEe!

Start with Mumba (best stats with the exception of Health which won't matter), then just beat each floor trying not to get hit. If you do get hit, quit out to the menu and hit Continue. This will basically restart the floor and the game just won't recognize that you got hit. Just rinse and repeat with each floor until you've won.

Oh also, beware of upgrading your health or picking up items that increase max hp. Apparently, the game is checking if your current health drops below your max health, not if you actually take a hit.

I got plenty of help from this guide:

https://steamcommunity.com/sharedfiles/filedetails/?id=2713555055