To perform a Focus Kill, you'll need to perform any kind of take down on any guard. You can have up to three Focus Kills at one time.
I earned this achievement as I was progressing through the story. Since I played the game on 007 difficulty, I died multiple times, therefore retries and checkpoints are acceptable if you find three guys and take them out. But I didn't have to do any of that; I just earned them along the way. The game does have a counter that shows up when you perform them, so you'll always know how many more you need.
So either play through the story or get three Focus Aims and kill three guys, then restart the checkpoint. The best way to earn this one is in the casino at Monaco. Make your way to the room with the Security Chief. There will be three men, one being the Security Chief, the second walking up and down, and another just chilling nearby. Once the guy that's walking has his back turned on you, immediately whip out your silencer, hold down LB and press RT. If you're fast enough, all three men should go down. Then restart and do it again until you nailed eighty kills. Once you do earn eighty kills, the achievement should unlock for you.
Have fun and good luck!