In order to make someone kill one of their allies you must first learn Possession (Level 2), which will cost a total of 8 runes, as well as Bend Time (Level 2), which will cost you 10 runes. Due to their high rune costs you will not be able to learn them both until Mission 3: House of Pleasure at the earliest—that is if you find every rune up until that point.
The most reliable method is to have a soldier shoot one of their allies with a pistol, and is the same method shown in the Harm’s Way guide. Mission 9: The Light at the End is especially good for doing this—which is the location shown in the video—because every soldier has a pistol. The first step is to locate two more soldiers in the mission.
About two seconds after an enemy points their pistol at you they will fire. It is the same delay for each and every type of enemy. The cast time on Bend Time is also about one second. For a kill to count, simply use Bend Time (level 2) a second after one of them fully extends their pistol and aims it at you, or reloads after firing. The moment bend time activates the target should have just fired their gun.
Immediately use possession (level 2) on the soldier that did NOT shoot the pistol; if you possess the soldier that fired it will count as a suicide when they die to the bullet. Walk the possessed soldier in front of the bullet (be sure not to walk into it), and position him a few feet away from it—not right in front of it otherwise it will miss—then release the possession. It will instantly kill them and count towards the trophy. If only one soldier remains immediately flee and find an additional one.
It is best to have at least five or six mana and health potions before attempting this and to save first. You should also save right after you perform a successful kill. Load up the save if you make a mistake and repeat the process until it unlocks.
To see a walkthrough of the the method being performed, please see the video below:
This trophy can also come naturally during your high chaos playthrough. Occasionally, if a guard tries to shoot you but there is another guard in between you and the shooter, his bullet will hit the other guard and can kill him. This is not a sure-fire way of unlocking this trophy, but it is possible as I earned the trophy this way.