Disable the Founders Island Missile Launcher

Objective: Take out the long range missile launcher
Head to the objective marker where you'll find a large missile launcher on a rooftop guarded by enemies. This is a predator encounter.
The rooftop has a tiered construction with five levels; the lowest level contains the missile launcher and is guarded by eight armed Soldiers, one with a Detective Mode Scanner. After taking down 2-3 enemies, the Arkham Knight will alert the remaining soldiers.
Use environmental factors like vent tunnels, the Remote Hacking Device on alarm panels and generators for distractions, and door locks to isolate enemies. Girders on the east side offer good vantage points and access to ventilation shafts. Breakable walls and corners can be used for takedowns.
Start by heading to the lowest level, dropping into the floor, and using tunnels to take down the three enemies there, prioritizing the one with the Detective Mode Scanner.

Objective: Lower the barriers protecting the missile launcher
Proceed to the fourth floor of the rooftop and enter the control room. Interact with the computer to lower the defenses, which also lowers all bridges to Founders' Island.
This action automatically switches you to Remote Batmobile Control. Upon crossing a bridge to Founders' Island, you'll discover five Cobra Drone Tanks have been deployed.
You must destroy all five Cobra Drone Tanks before continuing the mission. Use your mini-map to sneak up on each tank, avoiding detection, and shoot their weak spots. Isolate each tank and take them down one at a time, using the island's alleys and buildings for cover and to break line of sight.
Destroying a tank will alert nearby Cobras, so move away from the explosion site and wait for them to resume patrol patterns before engaging the next one.
After destroying all five Cobras, follow the GPS route to a ramp.
Use the ramp to leap to a distant building's roof. Enter Battle Mode, locate the anchor point at the top of the ramp, and use the Power Winch to pull it back and raise the ramp.
You will regain control of Batman in the control room. The room below is now filled with enemies: two Medics, a knife-wielding Brute, and eight Soldiers.
Maneuver in the ceiling to perform a Fear Multi-Takedown, ideally targeting a Medic. Once on the ground, fight all enemies, prioritizing Medics first, then Soldiers, and finally the Brute. Utilize environmental takedowns and available weapons.
After the fight, use the computer again to lower the shield.