Requirements: Shoot each organ with a lethal outcome at least once. You don't necessarily have to use a sniper rifle.
Organs that can be shot in the game:
Shots throughout the whole game count - not just during one mission. Remember that the shot has to be fatal; hence suppressed ammunition isn't the perfect solution here. However, "double shots" also count, i.e. a case when a wounded enemy is finished with the right shot, will also bring you closer to completing the achievement. The animation of shattering the enemy's insides doesn't always have to commence, but it doesn't mean that a shot has not been qualified. The information with points that appears after hitting a target will let you know what have you shot.