Dishonored Definitive Edition

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.

This is on the mission "Return to the tower". Once you've made your way into the tower, you need to get the second floor. You can blink on to the Chandeliers to easy get to the higher floors to reach the broadcasting entrance. There is a arc pylon that you need to switch off at the bottom of the stair case. ( I advice you to save before attempting it)
Once the arc pylon is off you can continue to the top of the staircase. The broadcaster will tell you where the Lord Regents audio log is, and it'll show on your HUD. You can use the chandeliers to get to the Lord Regents bedroom, there is no guards in his bedroom(No worries for unnecessary combat) Once you've gotten the audio log return to the broadcasting room and insert the audio log. Achievement will pop after playing audio log.

Here's a video for people that need a visual explanation: