(Starting this quest will fail The Institute quest “End of the Line”)
Fast-travel to The Institute and take the central elevator to reach the relay room. Talk to Z1-14 and kill everyone else in the room, including the scientists. Once your allies are relayed to the Institute, talk to Desdemona to receive the Fusion Pulse Charge.
You have to go follow the quest marker and enter the Old Robotics section of The Institute. Once inside, you can use the old terminal by the stairs to deactivate the turrets. Eliminate the synth resistance downstairs and continue forth.
As you make your way down, you'll stumble upon another Advanced terminal that you can use to deactivate the turrets in the main room. Before heading inside, activate the prototype sentry bot using the old robotics terminal by the doorway. The sentry bot is not a friendly but it will automatically attack anything around it. Destroy the synths and once done, take out the sentry bot as well to get valuable loot. Open the floor hatch then drop down. There's a generator with fusion core here so claim it then continue forth until you reach the door leading to The Institute Bioscience. As soon as you're in, the rebel synths will join the fight.
Beware of the Power laser turrets on the ceiling as it can cut through your damage resistance fairly easily. Take out the synths and exit the lab to reach the main area of The Institute. Kill the enemies inside then you'll get an update about accessing the terminal in the Director's office to override the lockdown. Access the elevator to reach Father's room. Before you access the terminal, you'll find him sick in his bed. You can pass two speech checks to get the code from him and help some of the survivors.
From the terminal, you have three options: Initiate the evacuation of the residents, initiate the lockdown override, and shutdown the remaining synths. The last option requires Father's passcode to activate. Choose whatever option(s) you want then regroup with your allies in the entrance of Advanced Systems. Enter the area to proceed.
Clear the room then proceed to the reactor area. Kill the last set of enemies here. Two legendary synths will be here as well and they carry the reactor terminal password. Loot the password from their bodies then access the reactor terminal in the walkway above. Before initiating the shutdown sequence, activate the radiation purge first to remove the radiation. Once the shutdown sequence has been initialized, the reactor's door will open, allowing you to safely place the pulse charge inside. Next, talk to Desdemona so you can be teleported out of the reactor chamber.
The younger Shaun will be with Ingram. Talk to him and decide whether to leave him or take him with you. Once done, talk to Ingram to be teleported to the detonation site. From there, activate the detonator to trigger the nuke and watch the cutscene. Next, talk to Desdemona to complete the mission.
Post-mission, you can go back to the HQ to get more repeatable missions from PAM and Dr. Carrington. Drummer Boy will also give you three vertibird signal grenades which you can use to have Tom pick you up using the hijacked vertibird.