This sounds simple, but it really isn't. The first thing to note is that there must be at least 5 players in your Fragile Alliance game, because traitor kills once you have died and spawned as an agent do NOT count towards this achievement. And you know that trick you see people using of setting your grenade to go off after you die so that you can get an instant revenge kill? Kills in that fashion don't count towards this achievement either, you must still be alive as a merc. One final note for those who don't read properly: the 2 kills must be in same ROUND, not session.
The basic mechanics of this, assuming 5 people, are: player A kills player B, player C kills player D, and player E then kills both player A and player C to get the achievement. Unfortunately situations where multiple players turn traitor in the course of the round and you are still alive to kill them are very rare; I played over 200 sessions and I think only ever had 1 shot at getting this achievement "legitimately", so I highly recommend boosting this with friends or willing strangers.