In order to get this achievement, you need to complete the entire Ally quest line for Sofia Daguerre.
Sofia (otherwise known as Commander Daguerre) is an Ally NPC introduced with the Wastelanders update added to Fallout 76 in April 2020. The initial quest "Crash Landing" should trigger automatically upon entering The Mire or Savage Divide. Sofia can be found at the "Abandoned Bunker" location in The Mire in the northeast corner of the map. Other locations in close proximity to the Abandoned Bunker are East Ridge Lookout, Vault 94, Red Rocket Mega Stop, and Abbie's Bunker.
Once you finish the initial "Crash Landing" quest, you'll get the option to construct Sofia's Ally Furniture at your CAMP, her USSA console. Construct that at your CAMP and she'll show up, and you can start on her Ally questline.
The framing quest "The Woman Who Fell to Earth" will remain in your Journal for the entirety of her questline. There's no quest marker for this one, so no need to mark it as active to track your progress. Instead, these are the individual quests you'll need to complete:
One Small Step
In Case of Emergency
Bring Home the Beacon
The Universe Conspires
Hope Remains
Search and Destroy
Heavy Eyes
Patently False
Privacy Violation
Contractually Obfuscated
Boot Camp
Past Expiration
No Brainer
Calling Long Distance
Who Sat Down Beside Her
Lab Rat
Mission Out-of-Control
For each of these quests, basically what you'll have to do is travel to a location, pick up an item(s) or destroy a target, and return to Sofia at your CAMP for a short conversation and quest rewards. Occasionally another NPC will show up at your CAMP to have a conversation with Sofia, and you'll have to sit through that conversation before being able to initiate the quest-completing dialog. Just be patient and the rewards for the questline are worth it.
All told, the questline should take 3-4 hours to complete uninterrupted. I finished it over the course of 3 days while doing other stuff.