Has to be done in one playthrough, you can not complete the game then replay chapters
The key targets are as follows:
High Overseer Campbell - Knock him out and brand him with the mark of the heretic.
Morgan and Custis Pendleton - Head to the Distillery and talk to Slackjaw. Investigate what he wants done, and get the Art Dealer's safe combination and he will take care of them himself.
Anton Sokolov - Just either sneak up and choke hold him or shoot him with a sleep dart.
Lady Boyle - Once in the mansion find and talk to a Lord Brisby and he will want you to abduct her. Then go buy a lady named Miss White a drink and she will tell you which color dress your target is wearing. Talk to Lady Boyle and tell her your here to save her life, followed by someone wants to meet you down in the celler...follow her down there and when you are out of the line of sight from everyone, choke hold her and bring her to the guys boat.
The Lord Regent - Make your way to the second floor and up into the broadcast tower. Talk to the man up there and he will give you the code to the Lord Regent's safe. Go to the Lord Regents bedroom access his safe and get the Audigraph. Head back to the broadcast tower and pop it in the audio slot.
The achievement will either pop then or at the end of the mission.