Dishonored Definitive Edition

From VeryNovelQ's achievement guide for the Xbox 360 version:

You can easily earn this achievement during the Lady Boyle party mission. Sneak past the guards and tall boy without being detected to get to the courtyard. Once you are in the courtyard, you will not be treated as hostile as long as you put away your weapon and don't use powers. Present the invitation you got from the art dealer's safe if you raided it, or you can pick one up that someone drops near the courtyard entrance.

Enter the party and talk to party guests to find out that you need to go to Lady Boyle's bedroom. The best way to do this via the side staircase off of one of the smaller rooms, rather than the large staircase in the ballroom. There are stairs going up and down, and there is a guard by the stairs going up. Either wait for him to leave, or move towards the basement stairs, hide, and possess him or blink past him. In any case, make sure you're not detected. Once you're upstairs, grab the clue in the bedroom that tells you which colour Lady Boyle is wearing (it is random).

Head back downstairs, making sure to evade the guard again if you didn't knock him out. Once you're back in the party, look for a man in a scarecrow mask. Talk to him and he will provide you with a non-lethal alternative for the quest, which is to knock her out and take her to the cellar (basement). Then, talk to Lady Boyle. You can convince her to either go to her bedroom (if you ask to get her a drink), or to the cellar (if you tell her she's going to be assassinated and you can save her). I would recommend the cellar. Anyways, follow her to her destination and knock her out or kill her. If you choose the cellar, bring her unconscious body to Lord Brisby.

Head back upstairs and into the party. Head outside to where you battled Lord Shaw (if you did that sidequest). There is a big gated area overlooking the river. To get out, blink up onto one of the concrete pillars (making sure you are not seen) and either blink down, making sure to evade the guard, or possess the guard. Make your way to the flood gate and it will close. Walk over top of the flood gate, hop into the water, and swim over to Samuel