During Mission 5 - Argent Energy Tower the second Rune Trial you come across is for killing 10 unwilling with explosive barrels. The rune trial specifically relates to the Equipment Power Rune. The barrels will not look like the typical red barrels from the game, but they count towards the achievement. Be careful and get some room between yourself and the barrels as you start this trial with 1 health and the explosion will kill you if you are too close.
Just wait for the enemies to get close to the barrels and shoot the barrels. You can replay the rune trial from the campaign menu once you have unlocked it in the mission.