When you're near the Trinity Tower, you'll pick up a radio broadcast. Listen to it to start this quest. Head to the Trinity Tower and prepare to fight off some supermutants. The objective of this quest is to get to the top of the tower. You have to take the working elevators and ramps until you reach the top floor. The floors are quite small and you should be able to explore them thoroughly. For the notable loots or locations, check out Trinity Tower's own page.
On the top floor, the named super mutant, Fist is waiting for you. Kill him and loot his body. There's also a Super Mutant Heavy Armor, steamer trunk, and a weapons workbench. You can get Trinity Tower Cell Key from the steamer trunk as well.
Use the key to free Rex and the allied supermutant, Strong. They'll head to the lift but don't follow them yet. Supermutant reinforcements will arrive at the scene so dispose of them. Now enter the cell to find more goodies, including the Melee Bobblehead on the table.
Join them on the lift and activate it. Kill any supermutant you encounter while going down. The lift can only go down to a certain point so disembark, kill the next couple of supermutants then ride the next lift on the other side of the building. Kill more enemies then continue escorting them down the tower.
Talk to Rex to complete the quest and get your reward. You'll get Reginald's Suit if your character is male or Agatha's Dress if female. Next, talk to Strong to make him your companion. You can send whoever is your current companion to a friendly settlement then give him the supermutant armor pieces you have recovered.