You can do this achievement separately or as part of the "Silent Assassin" achievement.
The Silent Assassin achievement in HITMAN worth 47 pointsComplete The Final Test unspotted. Kill only Jasper Knight, ensuring his body is not found.
I will show you the strategy where you get both achievements in one playthrough.
Jasper Knight has a personal guard and we have to distract this guard to kill Jasper without being seen. One of the best ways is to use your own weapon or a weapon from another guard which is also the achievement "Security Defeated"
Go to the left side of the base and run forward in the shadows to the pipe in the back of the building. Climb up and wait until Jasper and his guard left the room. Go inside and then put a weapon or your weapon behind the closed door on the ground and go inside the bathroom. Jasper and his guard will come back and discover the weapon.
The guard picks up the weapon and moves it into a crate in the hangar. Jasper is now alone so equip your Fiber Wire and assassinate Jasper. Pick up the body and put it in the dump in the bathroom. Now leave the building / base on the same way you came in. The achievement "Silent Assassin" unlocks during the cut scene.