When Freedom Calls

Pick up the Laser Musket from the corpse outside then enter the museum. Once inside, take out the two raiders firing from above then find your way around the corridor to the right. There's another raider waiting inside so take him out. Exit the room to reach the locked entrance. Check the booth to the right to find two containers containing valuable ammo.

The quest objective is found in the third floor of the museum. Before going there, there should be a Novice locked door housing a generator in the lower floor. Open the lock and you should be able to get a Fusion Core from the generator inside.

Kill the remaining raiders to reach the trapped People. Preston Garvey will explain the situation to you. You can get additional information from him by conversing him with different dialogue options. Sturges will tell you about the vertibird above and that you need a fusion core to activate the Power armor left there (which you should already have by now if you managed to pick the lock of the generator door in the basement or open it via terminal)

There's a RobCo Magazine on the table beside Sturges and a Perception Bobblehead on the table where Jun Long is leaning on. The bobbleheads will permanently increase the stat they represent once collected. Leave the room then head to the rooftop through the door in the same floor.

You'll find the Power armor on the rooftop as Sturges said. Place the Fusion Core behind and grab the minigun from the crashed vertibird. Drop down to the ground and take out the raiders. Shortly after, a dreaded deathclaw will appear. Even with the Power Armor on, this guy will tear you to pieces so make sure to avoid confronting it up front. Due to its size, it can't follow you inside buildings so make sure to fall back to one of the open buildings there and try to shoot it from there.

After killing the deathclaw, take out the remaining raiders to complete the objective. Make sure to check every raider corpse. One of them will have the Corvega Storage Key which will be used during a sidequest later on. Once done, return to the museum and talk to Preston to receive your reward. To complete the quest and receive your rewards, Preston and the others should arrive in Sanctuary. You can fast travel there and wait or you can just walk with them.