This is within Liam's missions, and is considered his "Loyalty Mission". ME fans will know what this entails, but in general, keeping up in conversations with all your squadmates as the game progresses and doing everything they ask of you goes a long way toward getting this done. The mission, called "All In", will get you the achievement once you complete it.
Key requirements for getting Liam's mission are in spoilers (since they involve places/missions):
*** Spoiler - click to reveal ***1. Progress through his conversations as much as possible.
2. Complete any and all missions involving him, including a mission to Aya where he has you do a few things in the marketplace.
3. Progress far enough in the establishment of colonies in Andromeda (I, for instance, completed Eos and Havarl, had Voeld to the point of opening its vault, but when I went back to the Tempest, this mission unlocked. I did it right away so I assume Voeld's vault opening wasn't needed.)
4. At least as far as I can tell, get to the "Hunting the Archon" Main Mission.
Side Note; Even if you blow through most missions and are just looking at this achievements to see what they mean, this one should be one to do. This seemed to be the mission the writers decided the dialogue could be slightly less serious throughout parts of the mission.
As with any guide, if people have confirmed they can complete things sooner than I did, feel free to comment below and I'll correct as needed.