You must take absolutely no damage between starting your run and jumping down the whole after beating the second boss. This means: you can't use Sacrifice Rooms (dark room with spikes in the centre), you can't enter Curse Rooms (indicated by a door covered in spikes), and you can't get hit at all. Even if you pick up a blue Soul Heart, taking damage to that still counts as damage.
Things that DO NOT count as "taking damage" (props to Insane Fallout on True Achievements)
-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
If you've unlocked Judas, it may be worthwhile to use him to unlock this achievement, as he hits harder than most of the base characters. And since you're not getting hit, the fact that he only has 1 heart is irrelevant.