Mission: One Shot, One Skill
As the mission starts, notice the deal going on in front of you as your main objective. The game has been updated to add Makarov in the car at the back left in the driver's seat so that it lines up with the events of Modern Warfare 3.
Wait for the helicopter to fly around and then for the wind to die down. After this, quickly hit the target of the mission and immediately shoot Makarov in the car after. You don't have a huge window of time, but if you miss, reload the checkpoint.