This is best done using cheats. Once you beat the game replay the helicopter fight in chapter 8 and give unlimited ammo for the RPG. Once you see the helicopter shoot it with the RPG and then use the rope to climp up and kill the pilot to get the trophy. Trying this without the cheats is a hell of a lot harder and a waste of time when it becomes so simple with cheats.
Destroy the helicopter without defeating any other enemies