To unlock the Dishonored Poetic Justice achievement or trophy, you will have to neutralize all key targets using indirect means. While the achievement description explicitly says Indirect Means, but it doesn’t necessarily enforce it on all missions, somehow.
Dishonored Poetic Justice Achievement
Below are all the main game targets that you need to eliminate to earn yourself the Poetic Justice achievement or trophy.
Assassinate him while he is trying to kill the Captain. Or choke him out when he enters the basement with the captain.
You can sell them to Slackjaw to serve as slaves. Talk to Slackjaw and complete a side mission her offers you. After doing that, he will take these twins as slaves.
You can knock her out and give her to her lover. You will find this man wandering on the first floor. Talk to him. Next, you just need to get Lady Boyle in Kitchen so that you can knock her out to kidnap her.
Go to the broadcast tower and talk to the broadcaster who will suggest getting Lord Regents tapes from his safe (935) and broadcast them over the air to dismantle his government. Doing that will not only complete the mission but will also unlock political suicide achievement.
Leave Daud alive in The Flooded District.
Knock out Farley Havelock during the mission The Light at the End. Leaving Teague Martin and Treavor Pendleton to their own devices will not affect this achievement
If you did all the stuff as mentioned in the guide above, the Poetic Justice achievement should be unlocked for you.