With Our Powers Combined

This is an optional Minutemen quest and will only be triggered by being hostile with the Brotherhood and after finishing the quests The Nuclear Option and Old Guns. Take note that this quest can still be triggered even if you assisted the Brotherhood in destroying The Institute.

Note: Taking Paladin Danse will only make you a temporary enemy of the BoS. You need to attack them indiscriminately then talk to Preston to start this quest.

You have to building one artillery piece in five different settlements you own. Once done, head to The Castle and talk to the radio operator to issue a strike order. Head to the northern side of the castle to witness the fall of the Prydwen.

After the Prydwen falls, the remaining Brotherhood of Steel forces will storm The Castle via vertibirds. Prepare the Defend the Castle. If your defenses are already heavy enough, you just need to sit back and relax as your turrets rip their vertibirds in the sky. Another option is to snipe the pilots with VATS to make the vertibirds crash. After the battle, talk to Ronnie then Preston to complete this quest and Defend the Castle.

The aftermath of Prydwen's destruction pretty much clears out most of the Brotherhood's presence, and what will be left is a smoldering wreck of the airship.