The Skyjackskillshot is achieved by killing a Vulture Gyrocopter's pilot while the vehicle is airborne. This is one of the hardest skillshots to achieve, as a steady hand is required to avoid destroying the Gyrocopter.
The best opportunity to perform this skillshot is with the first Gyrocopter encountered. When it first enters the room, time is slowed to allow Grayson to look at it and use the leash on it. At this point, you can use your PMC to shoot the pilot in the head.
This can be performed with the Head Hunter but is extremely difficult because you must either attack the pilot from the side or aim directly for his head. Any other approach will destroy the Gyrocopter.