Story related and can't be missed.
Upon exiting vault 76 you will get a waypoint to the overseers C.A.M.P. In her camp, the quest First Contact will begin. Follow the road south from the camp to the town of Flatwood and continue yor search for the overseer there. As soon as you finish the related tasks in Flatwood the achievement will unlock.
If you played the B.E.T.A and completed the mission, you might be required to create a new character and replay the mission for the achievement to unlock until Bethesda implement a way to get achievements retroactively.
While in the overseers camp, be sure to craft some armor and a weapon to unlock the related achievement A Fighting Chance (craft a weapon). The crafting supplies you recieved in Vault 76 will be sufficient to craft a weapon and some armor.
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