This achievement is gained by unlocking a mutation after completing the quest "Turn and Face the strange". This can be done on any difficulty.
To start the quest complete the main quest "The Beast of Toussaint" and you will be in a warehouse next to then river after fighting a vampire. Go up the street to the south and there should be a quest marker (about where my marker is on the map below). You do not have to complete the main quest, but it follows on nicely and smoothly if you do.
Go towards it and a cutscene should start. You will receive a message and start the quest. Follow the quest until the end in the laboratory (for help reaching it see puzzles below) where you will get the ability to press "y" in your character menu to develop mutations. You will need greater mutagens and skill points (2 skill points and 2 greater mutagens of either red, green, or blue), I found these in containers throughout the elven ruins and lab, so loot everything you can.
There are two puzzles in the elven ruins:
Open the door in the broken room with the rope. There are four plates on the walls that you can shoot with your crossbow. One to the right and one to the left of the door, one on the broken wall above the rope and chasm, and one opposite the last on the normal wall.
Navigate through the portals. The statues in the centre of the rooms face the portals you must go through. From the entrance to the room, go though the left portal. In the next room the portal is straight ahead, drop down towards the statue then climb up
to the portal. Finally in the last room stay on the floor you start on and follow it around, jumping over a broken section to reach the portal.
Note: a potential bug is that the achievement simply doesn't pop even though you have a mutation. Try using a potion of clearance, then doing a different mutation. Thanks to Bastiaen
for this bug and fix.