This achievement can be earned in the third part of mission 4, but is a bit tricky. Once you get into the mansion and proceed from the entrance into the first room, you do not want to pull the lever to start moving the pieces of the mansion around. Instead, use a crossbow or gun to shoot out one of the glass windows in the skylight and blink up there.
Head into the side behind-the-scenes hallway and follow it all the way to the end, blinking up into another hallway and onwards. You'll come to a room with a skylight, with open windows in the floor. Go past it and to the windows on the back wall. Carefully open one and use your crossbow to quietly eliminate the guard. Go through the window and take out the guard in the hallway to the right. Go in that direction, into the next room, and through it to the exterior balcony. Go to the end of the balcony, and blink onto the outside of the building and down to the lower area. There is a hatch you can open and head through the wall. Take the elevator to the top floor.
When you exit the elevator you will find yourself in the top balcony floor of the lab, with Jindosh pacing around a desk over to the right and a clockwork soldier patrolling between the desk and the doorway where you are. When the soldier is facing the other direction, use blink to move around the circular balcony to the left and then up onto the higher platform. Move in the direction of Jindosh.
From here you can reach him with your crossbow, one or two quick strikes will kill him and unlock the achievement. If you want to go nonlethal, use a sleep dart to knock him out, head over (avoiding the gaze of the clockwork soldier) to him, pick him up, and quickly go over the balcony and down to the floor of the main lab. Follow the directions to put him in the electrical chair, reduce the power of the other panels to allow you to turn on the chair, and then use it on him. The achievement won't unlock until he's completely disabled with the chair.
Alternatively, save and kill him to get the achievement, then reload to continue the non-lethal approach.