UPDATE: unfortunately this one seems to be glitched in some cases and the achievement doesn't pop until well after the required 10 kills or not at all. if someone has a solution for this problem, send me a message an i'll update the guide.
UPDATE: try Mission 5 first. Seems to have a higher success rate judging by the comments in different youtube guides. also "ThisOnes4Dixie o" wrote that it instantly unlocked on 5 when 7 didn't work.
Right at the start of the mission you will have the opportunity to kill two snipers. Go to the spot in the video and make a savegame. The snipers will change their position slightly from time to time, but you will always see them.
Your first shot doesn't blow your cover but you have to take the second shot pretty quickly or you get spotted. Load your savegame and repeat. Mission 5
Early in Mission 5 you will see a cut-scene. After it, go into the small room right next to you. Thats the spot were you can get the 10 Sniper kills.
Look out the window and wait for the enemy sniper on one of the rooftops. I highlighted the 3 spots he will pop up in the video. He patrols this roof and moves between 4 different spots. One Spot is on the backside and he will be gone for about 60 seconds.
Just wait for him to come back to the front side. As soon as he shows up make a manual save so you don't have to wait for him after loading. repeat this 9 more times and the achievement is yours.