This is one of the harder achievements of the "Don't take any damage" achievements
You can get damaged on all other floors just make sure not to get hit on the Depths or Necropolis
The best tips I can give you is to familiarize yourself with the enemies and their movement/attack patterns. This goes for the bosses as well. Be cautious with spikes and fires for any misstep can cost you a run.
Also if you are able to get a solid item that can do A lot of damage on the first couple floors, it should help greatly.
Purchasing from a Deal with the Devil Room does count as taking damage
If you are able to get The Bible, USE IT, it kills Mom instantly thus saving you a ton of heartbreak
These do not count as taking damage
-Using the Blood Donation Machine or IV bag.
-Damage taken from the Devil Beggar.
-The "Bad Trip" or the "Health Down" pill effects.
-The Razor Blade and Blood Rights items.
-Using a "Health up!" pill.
-Taking damage while under the effect of Holy Mantle