Obviously, this takes place in the Timur the Tinkerer level where you need to beat it using only trap kills.

NOTE: YOU DO NOT NEED TO KILL ALL ENEMIES IN THE LEVEL TO GET THIS ACHIEVEMENT

When you start the level, immediately go into the sewer pipe in front of the door and pop out of the vent inside. Then, deactivate the front door trap, take the shotgun, and blow up the mines with it.

Proceed through the door and ignore the first light switch trap. Right in front of the couch is a floor trap that'll set off three grenades. Step on it then run away until the grenades detonate.

Go to the door trap afterwards, knock on the door to trigger the goon, then take cover behind the couch so that the stray bullets don't hit you as well as the goon.

Go into the next room and flip the light switch so that the two goons upstairs get killed by the trap. There are two other goons in the same room, but you can easily bypass them by going into the vent downstairs and popping out of the one upstairs directly behind them.

While they're busy checking out the mess, go into the next room and into the floor vent and pop out of the SECOND wall vent. Enter the next floor vent, pop out of the FOURTH wall vent, and disarm the shotgun trap right next to you.

In the floor above the next room is a sledgehammer goon. All you need to do is quickly run up the stairs to get his attention, run back down, and then run back up again when he follows you down.

Then, all you need to do is assasinate Timur by finding the right switch in the room with, well, the billion light switches. Not too hard to miss. The switches are completely randomized, but make sure you flip the one with TWO wires leading into Timur's room.

After he's dead, get the contents in the safe, flip the red lever next to the floor vent, and exit via the rooftop. BOOM, achievement unlocked!

Hope this helped!

Editor's note: For some stupid reason, it wouldn't allow me to take in-game screenshots, so that's that.