After watching the film, you left soo much on the table Pink. After you shot Nate's turret mounted machine gun away, drive your vehicle into the confines of Nate's vehicle, matching every move he makes and staying clear of his front hull machine guns. His turret cannon will never be able to hit you either. Then, when another teammate of Nate's comes out and fires at you, they die because they hit Nate with kill shooter on in the arena. Sometimes you can shoot one of the tracks off with your machine gun and then they just sit there with no option but to end mission, giving you a kill and you run off to safety while they are respawning at the hanger.
Cheers, One-eye