The absolute easiest way to get this involves, sneaking into the apartment, opening the panic room, erase the camera footage, and then interact with the computer to start the mission.
As soon as the target enters the building, hide in her bedroom closet. Wait about 5 minutes for her and her boyfriend to enter, and begin preparing for sleep. As they enter the washroom, sneak out of the closet, go into the room to steal the keys, then quickly go to the washroom and garrote the target with fiber wire. Drag her to the closet to hide the body. Jump out of the bathroom window and use the keys on the door beside it. Sneak into the panic room, through the garage and back to the shore. Use a fragmentation grenade or the SUV as a distraction and then exit the level using the boat.