As the achievement states, you'll need a Professional Hitman. the amateur hitman doesn't work.
you can randomly find one while roaming around or you can get it by turning the Nine Elms district into defiant state. (finish all the red icon missions and the mission that unlocks after)
simply switch to the hitman and sneak up on enemies and press X to perform the stealth takedown. repeat 5 times.
EDIT: the takedown must be the done while un-armed and with the hitman wire tool.