The Nuclear Option (Minutemen)

Talk to Sturges to learn about this secret entrance leading to The Institute. Fast-travel to Ticonderoga and find the underwater pipe. Take note that this area is highly irradiated so make sure to use high anti-radiation gear and Rad-X.

Once inside, you can access the red steamer trunk behind the security door via hacking the advanced terminal. Operate the keypad on the wall to open the grate in the Water pipe. Go through the pipe and you'll be dumped in the next area.

Follow the main path and you'll encounter a couple of laser turrets along the way. Destroy them and continue forth until the end of the tunnel. Open the hatch and continue to the next room. Collect the loot inside and carefully proceed through the inflow tunnel. There are a lot of ghouls here so make sure to proceed carefully.

After eliminating the ghouls, continue through the tunnel until you reach a part where there are synths. You can either hack the Expert terminal nearby and open the security door or enter through the breach on the wall in the end of the tunnel.

There's a working generator in the generator room with a fusion core. Pick the Expert lock and explore the other rooms. There's no local map in the area so you have to rely on your compass. From the Expert locked security door in the generator room, turn right then right again to the SE to find another room. Theres' a weapon bench, robotics terminal (where you can eject 4n1m4l's holotape), and Expert security door with minor loot inside. Across that room is a classroom with a novice wall safe and med kit on the desk.

Follow the quest marker and you'll find a room with a Power armor station. Next to it is narrow room with a stealthboy, some fusion cells, cryo grenades, and institute weapons on the table. Kill the synths in the next room then go through the next pipe to reach The Institute itself.

Open the hatch and you'll be back again in the relay room. Access the relay terminal then load The Institute Relay Targeting Sequence. Once loaded, select the option for Remote Relay to call in reinforcements. Talk to Preston to get the Fusion Pulse Charge. You'll have to reach the Institute's reactor to plant the charge there. Also, you'll get the optional task to issue the evacuation order to save as much lives as possible.

Old Robotics

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.

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. If you still want to work with the Railroad post-mission, you have to issue to evacuation order. Failure to do so will make them automatically hostile towards you. Choose whatever option(s) you want then regroup with Preston in 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 Preston 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 Sturges to be teleported to the detonation site. From there, activate the detonator to trigger the nuke and watch the cutscene. Next, talk to Elder Preston to complete the mission.