Rat Man dens are partially hidden areas with red writings and handprints on the walls. Check the notes at the bottom of this guide before trying to find them.
Here are the locations:
(Starting a new game from chapter 8 works fine)
#1 - Chapter 8 - Testchamber 16
After the first three turrets there is part of the wall sticking out with two boxes behind it. Move the boxes and go behind the wall for the first Rat Man den.
#2 - Chapter 9 - Testchamber 17
After getting your companion cube you climb up, travel along two corridors with energy balls and then drop down into a room. In this room is a piece of wall sticking out. Portal behind that for the second den.
#3 - Chapter 10 - Testchamber 18
After portalling across the first gap it's on the left, crouch to get in.
#4 - Chapter 11 - Testchamber 19
Quite a while after you start your escape you will walk along a large pipe then drop down what looks like a large well (the game loads during the drop). Turn to the right and go into the alcove.
#5 - Chapter 11 - Testchamber 19
Soon after #4 you will be in a room with 3 turrets. Shortly after there is a single turret with a door that opens when you pick up the turret. Go through the door, to the end of the room and enter the alcove on the right to find the final den.
Notes:
- You need to find all these on a single playthrough as starting a new game or loading another save will potentially change the counter.
- The counter can be found by pressing start and selecting achievements.
- The same counter can be used when you think you've found a den and want to check the game has counted it.
Extra notes:
Neko Pounce says "If you get one, and then die before it saves, You have to get it again for it to count, that kept happening to me."
Xonatron says: "just verifying that a new start does change the count. it's all to be done on one play through."
maiden of haste says "reloading the same save will reset the counter!!!"
Here is a video, thanks to Xonatron & Sickeder666: