Attaining the rank of Eliminator requires you to complete two assignments: “Scheduled for Execution” and “The Assassinated Man”.
Scheduled for Execution – This assignment is given to you by Vicente Valtieri in the Sanctuary in Cheydinhal. You must kill the Dark Elf Valen Dreth in his cell in the Imperial City Prison. Sneak back into the Prison via the same entrance that you escaped from at the beginning of the game. Follow your map and make sure that you avoid the guards that are wandering around. Once you’re back in your old cell, you’ll hear a guard talking to Valen Dreth in the cell across the hall. Wait until he leaves and then open the door of your cell and shoot Dreth with an arrow. If you’d like to kill him face-to-face, go to the end of the hall and take the key to his cell. Grab the Imperial Prison Key as well. Once he’s dead, go up the stairs, exit the Prison, and return to the Sanctuary for your next assignment.
The Assassinated Man – This assignment is given to you by Vicente Valtieri in the Sanctuary in Cheydinhal. You must fake the assassination of Francois Motierre in Chorrol. Go to his house and he will explain the situation. When the hitman, Hides-his-Heart, arrives, slash Motierre with the Languorwine Blade. He will appear to die and Hides-his-Heart will attack you. Flee the city and then wait twenty-four hours. Go into the chapel and revive Motierre. Unfortunately, this will trigger by some zombies, so you must defend Motierre before escorting him to the Grey Mare Inn. Talk to him once you get inside and then return to Sanctuary. The achievement will unlock as soon as you start the conversation with Vicente.