Much to Learn’ Achievement Guide
Start with a low range weapon, switch to manual targetting in settings and try to kill as few enemies as possible. Then I sold my weapon and bought armor/shields. Got defeated on floor 4 (no way to heal up without hitting stuff).
Started a few new runs and tried the same thing – I eventually got the achievement after floor 1.
Looks like it can be done over multiple runs – you just need to play a total of 5 floors where you don’t get enough exp for a level up (no additional inventory slots reward is your indicator).