Borrowed from Chimaera36's guide for the Xbox 360 version:
This is awarded if you pursue the non-lethal path for the mission where you need to eliminate the Lord Regent at Dunwall Tower.
Go to the broadcast tower and talk to the announcer, who will give you the combination to the Lord Regent's safe. Go to his room and get the confession Audiolog from his safe, bring it back to the tower and place it in the machine.
You get the achievement, complete the mission and get possibly the most backstory-enlightening recording of the game.