Several items in the Binding of Isaac allow you to skip a level without facing the boss (We Need to Go Deeper and the Teleport! item, though teleporting is a less reliable form of level skipping).
I've managed to get all "no damage" achievements except the one for The Depths, mainly due to the abundance of Leapers on those levels. Whenever I unlocked one of said achievements, it was always the instant I defeated the boss on the second floor for that level, making it seem like the two are tied together.
So I was wondering, suppose I simply skip through the second level without having incurred damage on the first (possibly skipping some or most of it as well), will I still get the achievement?