The Binding of Isaac: Rebirth

Posting this as a clarification:

You cannot take any damage, that means no damage to red hearts, soul hearts (blue), sin hearts (black) or eternal hearts (white). So literally, don't take damage.

As for the actual achievement itself, it becomes easier to obtain after playing the game for a bit. You'll be more aware of attack patterns, enemy behaviour and are more familiar with bosses. Trying it on the first two floors isn't that hard, since you'll face some of the easier enemies here, but depending on your build that run, it could be just as easy to get it on later floors. Don't get discouraged if you take damage on early in the game. I ended up with a build that let me pretty much kill all enemies in one hit, bosses in 3-4 and got through Utero/Womb without taking hits and unlocking the achievement near the end of that run.

I earned this with a Devil Item. It's called "We need to go deeper!" I started a new level after going through the trap door. Once on the next level, I activated it. Easy peasy when RNJesus blesses Issac.