This quest is considered a main Minutemen quest, although it is avoidable. The key is to make enemies with The Brotherhood of Steel while being allied with The Minutemen. This can be done even after the conclusive events of The Nuclear Option (The Minutemen). The most direct way would be to kill a key staff member like Paladin Danse or someone more senior ranking on the Prydwen.
The next step is one of the most resource-intensive objectives in the game. Using various allied settlements in The Commonwealth, your task is to build artillery cannons on five of those settlements.
Using the workbench menu, the artillery option will be found under the Special section. We found that oil was the most scarce resource, though we remedied that with visits to shops in Diamond City. For every cannon you build, you will need to assign a local settler to man it. If you've forgotten how to assign a settler, just highlight the person during workbench mode.
With all five artillery cannons built and assigned, head back to Fort Independence. Speak to the Minutemen radio operator to initiate the attack on the Prydwen. You'll have a brief minute to enjoy the fireworks in the distance as the airship is obliterated.
Remember, the Prydwen is a flying ship that holds smaller flying ships. Now that The Brotherhood's main base is destroyed, the survivors are out for your blood. Riding a fleet of Vertibirds, the remnants of will quickly make their way to the fort.
This reprises the Defend The Castle quest, except that the belligerents have changed. Any army of power armor is a formidable force. Hopefully the defenses you already built for the last siege are still there. The good news is that, even if you're low on ammo and supplies, you can actually fast travel to Diamond City in the middle of the fight. Whatever your preferred tactics, speak to Preston Garvey after finishing off The Brotherhood to complete the quest.