Ancient Root

Find a ramp and use it to get inside the port yard. More drones are waiting for you inside so take them all out as well. Find the freight elevator and remove the cover using the power winch. Power up the controls by revving your engine.

Once you've reached the lower ground, run along the tunnel walls to get past the obstacles. Continue forth until you reach a closed gate. Leave the Batmobile and enter the grate. Go through it and use your RHD to temporarily blind the drone. There's a stationary drone on the right side alcove and a roving one nearby. If you have bought the Disruptor upgrade that will destroy any drones that detects you, it will be useful here as well. Behind the drone in the right is a Riddler Trophy you can pick up easily.

Continue forth, and destroy/blind the roving drone and continue until you see the control room. Grapple on the overhead metal beams and find a way inside the room to open the gate. You'll be remotely controlling the Batmobile. Use it to destroy the drones along the way. Once clear, unlock the second security gate and continue forth.

Lower the cargo ramp on foot and use that as a ramp for the Batmobile to run on. You'll encounter yet another gate. Back up a bit then speed up to run on the tunnel wall past the gate and the broken part of the road. Once you see the cargo loading bay of the tunnel, position the Batmobile on the other end of the ramp. Exit the vehicle and find another control room where you can lock the cargo ramp. Also, on top of that control room is another riddler's trophy.

Now use the cargo ramp to get past the flooded part of the tunnel. Continue along the path and use your sonar blasts to track the root. Upon reaching the core, hold your sonar blast to wake it up.