To cause an unintentional suicide you must first learn Possession Level 2, which will enable you to possess humans. After doing so you can possess a human and cause them to perform a task that results in their death. The easiest way to do this is by having a soldiers shoot themselves, which also requires Bend Time Level 2. 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.
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 them (or someone other than the person that fired the shot for Manipulator). Turn them around, walk around the bullet, and then position them a few feet away from, but still in front of, the bullet—not right in front of it otherwise it will miss—then release the possession. It will instantly kill them and count towards the trophy. It is best to have at least five or six mana 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 one method being performed, please see the video below: