During several of the missions you will be given the option to neutralize your main target through non-lethal means. Doing so is required for completing the Clean Hands trophy, as well as achieving a low chaos rating. There are a total of four main targets that are to be eliminated via non-lethal means to earn this trophy, so please refer to the spoiler for walkthroughs on how to eliminate those targets.
High Overseer Campbell - Sometime in this mission you will have to free someone chained in a courtyard. Once you do, climb to the top of the fence behind him that is bordering the castle. At the top of the fence you will overhear a conversation between two guards, that will trigger the objective for a non-lethal elimination. Continue the mission and locate Campbell, at which point you must knock him out (via sleep dart or choke). Pick up his body and make your way to the torture chamber, where the branding item is located in a nearby room. Use the item to brand High Overseer Campbell with the Heretic’s Mark, which will complete the objective.
The Pendleton Twins - this one is rather easy as it is tied directly with Slackjaw’s missions. Find and speak to Slackjaw during mission three and complete both tasks he will give you. Doing so will automatically take care of the Pendleton Twins via non-lethal means. Refer to the “Street Conspiracy” trophy for a walkthrough of each of Slackjaw’s missions.
Lady Boyle - Talk to the guests of the party to learn which Boyle is wearing which colored dress. Explore the rooms further until you come across Lady Boyle’s lover. Speak to him in private and he will inform you that he knows of your mission, and proposes to you that if you bring Lady Boyle to the cellar alive, rather than assassinating her, he will make her disappear. He will identify exactly which Boyle is ‘Lady Boyle’. Once you have her marked speak to her to the point where she will lead you upstairs to a bed. Now choke Lady Boyle, pick up her body and travel to the bottom of the stairs you just came up. If you come across any guards use Bend Time to get by them. Take an immediate right when you enter the kitchen, and follow the path to a switch that opens a gate to the cellar. Carry her body into the cellar to find her lover on a boat, who will then take her from you.
Lord Regent, Hiram Burrows - Upon arriving at the tower Samuel will inform you about the broadcast tower that all of the propaganda is aired on, opening up an optional mission to travel to it and investigate.
After making your way through the heavily guarded yard you will finally reach the mansion. If you entered through the frontmost method you will find yourself in the main lobby. Once you do use Blink to ascend the chandeliers and sneak into the Lord Regent’s chamber. You will see a safe to your right; the combination is 935. Open it and take out Lord Regent’s confession audiograph.
Exit through the balcony and Blink towards the left hallway. Turn right and travel down the hallway until you see the Arc Pylon. If you have Bend Time 2 use it to walk past easily, otherwise use Blink to travel just above it onto the stairs. Walk up the stairs and activate the broadcast system to complete the objective.