-( Story related, cannot be missed )-
^ Despite this, this is also a faction-specific achievement. If you're wishing for information on this achievement's main mission, read the spoilers.
*** Spoiler - click to reveal ***Faction: Institute
Mission: Mankind-Redefined
Institution introduction leads to: Synth-Retention, Battle of Bunker Hill, and then to Mankind-Redefined.
By completing Battle of Bunker Hill, you will need to return to the Institute and go to the conference room to debate with the other Department Heads. After the discussion, you will acquire the use of a new companion and complete this mission, setting you up for the next, Mass Fusion (near the Point of No Return for certain factions).
Disclaimer: If you find anything wrong with this solution, please leave a comment so it can be modified rather than leaving a negative vote and not discussing why. Thank you, I appreciate the chance to continue helping others.