On this page of our game guide to Batman: Arkham Knight we explain how to infiltrate the tunnel network under Miagani Island. The main part of this task is a walk-through combined with the use of various Batman gadgets.
Your next destination is the entrance to the tunnels. It is located in the central part of Miagani Island. Glide towards the entrance and summon the Batmobile when you're near. Now, a rather difficult battle awaits you. You will be facing several dozen enemy tanks. When fighting, avoid staying in one place for too long. To reduce the number of targets that you need to face at one time, you can go to the narrow alleys nearby. This will make it more difficult for the vehicles to reach you.
When the battle is over, go back to the place marked by the game, park the Batmobile and go inside the tunnel, when the passage is open. Stop near the first barricade, look up and use the Winch on the large ventilator. Pull it out and use the grapnel to reach the hole.
Listen to a conversation with Robin and spread Explosive Gel on the planks nearby unlock the passage. Do the same near the next wall and go inside the ventilation shaft. After reaching a large working ventilator, select Line Launcher in the inventory. Aim at the wall on the other side. Slide on the rope to the shelf that you can see far away
Now it's the first time that you have to use another one of Batman's gadget, the Remote Control Batarang. Use detective mode to locate an interactive switch (behind the fence). The Batarang has to fly through the hole in the wall, located to the right of the switch (control the Batarang as it flies and hold the key/button responsible for decreasing speed if needed).
When you hit the switch with the Batarang, a passage will open. You need to get to it right away using the Line Launcher. Climb onto the shelf and approach the edge. Choose Remote Control Batarang again. This time, you need to send it to a hole in the left wall (it is well visible). Behind the hole, direct the Batarang towards another switch.
Select Line Launcher and aim at the shelf nearby. When the rope reaches the target, immediately press the key/button responsible for slowing down when sliding. Turn the camera to the left and use the Line Launcher again on the wall shown in the picture above. It will change your course 90 degrees.
You will reach a large tunnel with a very big group of enemies inside. Don't try to attack them, because they are enemy tanks parked nearby and they would kill you immediately. Instead, start jumping from one vantage point to another and look for a ventilation shaft located very high. Reach it using the grapnel. Start going through the shaft and ignore the enemies. You need to get to the room marked by the game. When trying to leave the shaft, you will be attacked by Arkham Knight (you cannot escape it). Watch the cut-scene.