As part of normal story progression, Adam will meet up with the Fixer as he prepares to complete his mission. To unlock the achievement, Adam must prevent the Fixer from being killed and then talk to him. Regardless of the choice made during that final conversation with the Fixer, the achievement will unlock immediately following the conversation.
If the Fixer is killed, quickly press
and load the latest auto-save. This will allow you to redo the sequence, hopefully, with the Fixer surviving. There are two ways to prevent the Fixer's Death. One is to persuade the would-be killer to put down his gun. That can only be done if Adam has the use of his augments. The other way is to neutralize the would-be killer--lethally or non-lethally.
The final segment of the game leading up to the final encounter with the Fixer, begins with Adam releasing Mejia from solitary. Adam must turn off the transport tracking system and override two anti-aircraft turrets. When he accomplishes those objectives, he can proceed to his departure point where he encounters the Fixer--unlocking the achievement if he can keep Fixer alive and have a conversation with him.
Once Adam turns off the transport tracking system, he activates an optional side objective. The below two videos show Adam proceeding from solitary, accomplishing his tasks, and unlocking the achievement nonlethally. The first video shows the optional side mission and also includes a decision point at the 8'40" mark where those that are not interested in the optional side mission can go directly to the second video. Doing so, skips the side mission and continues straight to the achievement:
The first video picks up the action from solitary confinement. The video that accompanies the below solution shows one of the paths to solitary if required for reference:Solution for Objection! in Deus Ex: Mankind Divided