Use the K.A.R., ignore Kiril, keep killing Homeless Mercenaries until Rook 25 comments something down the lines that "you don't have to kill them all," then kill/capture Kiril. The associated Kiril achievements (Mercy for the Merciless & Kill Me, Will You?!) will pop immediately. After they are done commenting on how you handled Kiril, they'll comment on how you dealt with the Homeless Mecenaries. If they're all dead this achievement will pop.
Another way to measure progress on this is, for every kill, Rook 25's alignment goes down one for a total of -11. Yanko (the door guard) doesn't count towards Rook 25's alignment. It is unknown if Yanko counts for the mercenary kills not that it is worth the bother to distinguish him from the rest.