On this page of our game guide to Batman: Arkham Knight we explain how to gain access to the subway network. We indicate the proper road you should take and warn you about all difficult traps that may appear during your drive.
Note! Before you start this mission it is good to unlock new combat skills and (most importantly) Batmobile's defense, as they will prove very useful here (and also some time later).
Start the patrol from Port Adams. After getting there wait until the gate is open and get ready for the most demanding fight so far, in which you will have to take on enemy tanks and flying machines. Most importantly get away from the main gate as quickly as possible and find a spot where enemy forces will have it hard to flank the Batmobile. Just as you did previously, apart from firing at enemies, use the Drone Hacker (take control of larger and more resistant enemy machines), EMP charge and the dodge engines.
If possible you should also destroy flying drones as quickly as possible, because they are much more mobile than tanks. Moreover, from time to time they bomb the area with rockets, which are harder to dodge (stay away from red circles appearing on the ground).
When you secure the first part of the port, look for a ramp that will get you to the location with containers. This is where you will encounter more enemy machines, fortunately, in the meantime the Batmobile energy bar should have regenerated, so you will not be left defenseless. After destroying about a dozen tanks look for the closed elevator door. Use the Winch on the door and when you manage to tear them out, grab the elevator mechanism. Drive close to the mechanism and properly operate the gas pedal (the rev has to be within the orange area on the tachometer) to move the elevator and get to the subway network.