First off you must play normal mode, not easy.
Shoot your machine guns in short bursts to shoot down his missiles, while hitting him with your own. If you run out of missiles, you should be getting more from shooting his down. If not, fire at him with short bursts on your machine gun, leaving enough heat left over on your meter to not overheat defending yourself.
Play it careful and you will eventually down him without taking a single hit, and gaining the achievement.