The first time you fight Arkham Knight will be at the beginning of the main story, when you rescue the lost workers at ACE Chemicals. When going back with one of the workers, you will be stopped by the villain, who is controlling a flying machine.
At the beginning of the battle, don't bother attacking the flying machine controlled by Arkham Knight. Instead, focus on destroying all the tanks on the square. Besides avoiding their attacks, you also need to watch out for the flying machine. The game displays circles on the ground, which mark the area when missiles will explode. Just like in the case of tanks - red color means that you're in trouble. Move away from the spot and use dodging engines to do it quickly.
After you deal with the tanks, Arkham Knight will shoot several missiles directly at the Batmobile. To avoid being hit, destroy them on the way. Use Vulcan Gun to do that.
After you avoid the first attack, start damaging the machine. Its energy bar can be seen in the top-right corner of the screen. You can lower the bar by shooting from your 60mm cannon. It is very important to constantly move from one place to another and to use dodging engines, because Arkham Knight will perform his attacks regularly. Shooting the machine down will end the fight.