Story Related, Unmissable
Once you've collected your gear from the locker next to the door, re-equip everything and make your way to the President’s office. Along the way you will have to fight several Enclave Soldiers, Officers and a few Radroaches so be careful. There will be lots of weapons, ammo, armour and health items lying around so make sure you pickup as much as you can carry as you won't get another chance. Don’t forget to pick up the Energy Weapons Bobblehead from Colonel Autumn's desk on Level 2 before entering the Control Room as this is your only chance to get it! Fail to pickup this Bobblehead and you will either have to either load an earlier save or start a new game from scratch.
Soon after you meet the President, he will order you to take a vial of Modified FEV virus to plug into the Purifier at Project Purity (whether you use it or not is up to you but you can't exit the President's Office without it). After taking the vial, you will get the opportunity to persuade the President to kill himself and blow up the base. Regardless of which option you choose, you'll be allowed to leave the base.
After exiting the base you will run into Fawkes (if you freed him from Vault 87) and he will ask if can join you (only if your Karma is Good). After dealing with Fawkes, Fast Travel back to the Citadel and make your way to the Science Labs where you will witness an argument between Scribe Rothchild, Elder Owyn Lyons and Sarah Lyons. Once the Argument finishes, Rothchild will ask you about the Enclave and at some point the Modified FEV virus will be mentioned and you will have the opportunity to either lie about what happened to it or hand it over to him for disposal and a Karma boost.
After Rothchild finishes with you, Sarah Lyons will make you an honorary member of the Lyons' Pride and will give you a choice of either a full suit of Power Armour or a full suit of Recon Armour, after which she will ask you what to do about the Enclave. This where you need to be careful because if you don't have the Broken Steel DLC or have a save file backed up somewhere, choosing to attack the Enclave will cause "The Take it Back!” quest to start and take you to the point of no return. Your best option is to say you need a minute to sort some things out, to which Sarah will say hurry up (or something similar) and you will exit the conversation and the trophy will pop.