Semper Invicta

Semper Invicta is a Brotherhood of Steel main quest and an achievement/trophy in Fallout 4.

Detailed walkthrough
Once the Survivor completes the quest Call to Arms, this one will show up automatically, asking the player character to go back to Cambridge Police Station and talk with Danse.

After the discussion, Danse asks the Sole Survivor to help both Rhys and Haylen doing their respective jobs:
 * Cleansing the Commonwealth (repeatable)
 * Quartermastery (repeatable)

Once either of the requisite quests have been done, the quest The Lost Patrol may begin after talking to the Lancer Captain.

This quest will be marked as completed once both requisite quests have been completed once each. The requisite quests are repeatable whether or not this quest has been completed.

Behind the scenes
Semper invicta is Latin for "always undefeated," the motto of Warsaw, Poland since World War II.

Bugs
If Paladin Danse is spared during the quest Blind Betrayal, Haylen can be removed from the game upon completion, making it impossible to complete this quest without use of console commands. The quest marker will still be attached to her location, but as she is disabled and under the world, there is no way to interact with her, or even reach her. This can be addressed by entering, followed by , and finally. She should then be able to give the player Quartermastery as normal.