Enter the Batmobile and this time, raise the drilling platform again so that the Batmobile can reach the elevated tunnel. Use the fuse on foot to lower the gate and continue forth in the Batmobile. After a short while, the Arkham Knight will appear with a drilling tank. You don't have any way of facing him head-on so escape further into the tunnels.
You'll eventually reach a tunnel maze. What you need to do is lure the Arkham Knight in the dead-end tunnels with red markers. You need to drive fast and carefully as you go through these tunnels. This is the only way to damage the Knight's vehicle. The Arkham's Knight vehicle doesn't appear on radar so you have to gauge the distance as displayed in your screen. You can also lure him in by shoot at him when you're already facing the tunnel you'll lure him to.
After depleting his tank's HP, Alfred will be able to disable the lock on the door. Head there and use the power winch to remove the ventilation shaft's cover. Get under The Shaft and eject-glide yourself, watching in mute horror as your precious Batmobile gets shredded to pieces.