ok this cheevo is very simple however alot of people, myself included didnt get this when trying for it.
This is due to the fact that like other solutions state you may not use any explosives like grenades or explosive barrells.
Also you may not use any of the kill moves, (this is where i went wrong on my playthrough)
Having repeated what the other solution say, what they dont say is:
By far the easiest level to get this is the 1st level on recruit difficulty.
You have unlimited ammo for your pistol (which i didnt realise till the last level when playin on elite difficulty) so try for head shot but if needed just go to town on the enemy and fire an entire clip into them if you like.
Level 1 has very few enemies and NO explosive crates to ruin ur day.
The only bit to watch out for is when you are near the mole you will go through a room and a wall will explode and 1 enemy will try to rush you. shoot him quick as when he gets close it can be tempting to pull off a kill move.
*EDIT* from reading other comments and sites it sounds like if you perform a kill move by accident and reload your checkpoint then it cancels the cheevo and you will have to start the level again. Can any1 confirm this