Quote Originally Posted by valho View Post
Well you don't have to map it though as I got turn II and III mapping achievement without even running thorough the whole place, I just clear it and got the achievement.
the coils 2 and 3 maps in huge chunks, coil 3 per floor i believe. Coil 2 only has 2 portions: the boss & mini/boss area (everything that you can see on the map as soon as you enter), and the 2nd portion is the small corridor to turn 3, which is inaccessible unless the boss is dead.

So indirectly, the mapping achievements do show your progress.