Start following the car driven by Gordon. Soon, there will be two enemy armored vehicles following him as well. Don't switch to Battle Mode, but stay in Pursuit Mode instead. You need to mind two things: Firstly, observe the beams that show enemy attacks and use dodging engines to quickly move to the sides. Secondly, try to stay in some distance from enemy vehicles, which will allow you to lock the target. After the targeting process is complete, press the key/button responsible for activating the Drone Hacker.
Every enemy armored vehicle needs to be hit with the Drone Hacker three times. At the end, park the Batmobile in the place shown by the game and wait until Gordon gets inside.