This achievement is story-related and cannot be missed. However, there are some important things that can happen during this mission, so I will outline what can go horribly wrong. This will be filled with spoilers, so you have been warned.
Maybe make a backup save before starting this quest, just in case you're unhappy with the results.
*** Spoiler - click to reveal ***The conditions for the mission's outcome are actually determined before you set out on the 9th main mission "Short Sighted," which will affect the locations of your favorite and least favorite Constellation members during the coming crisis. This part by itself does not determine the mission's conclusion, but make sure to pay attention to where the different crew members end up.
After the 10th mission "No Sudden Moves," you will return to the Lodge to drop off the artifact, per usual. This will trigger a forced cutscene with Noel. Punchline: Constellation is under attack! You now are presented with a choice: either defend the Lodge or book it back to the spaceport and fly to The Eye.
This is the critical step: a party member will die at whichever location you don't go to first. So you need to pay attention to where your most valued teammate is. For me, it was Andreja who was on The Eye. If you want to make sure this companion is saved, go through all of the dialogue options saying that you will rescue The Eye. Then the moment you can move, head immediately for the front door. You'll have two conversation choices where you are asked if you're sure you want to leave. Say yes, then hightail it to your ship and take off. After checking on your crewmates on The Eye, you'll be told to return to the Lodge. Upon returning there, the person you had the worst relationship with will die in your uncaring arms.
If you decide to stay at the Lodge, simply wait a moment until you're told to check on one of your companions. An unwinnable firefight will ensue and you'll be forced to flee to your ship. After returning to The Eye, you will instead find a crewmate there who's given up the ghost.
Punchline: everyone will be saved at the location you go to first. Someone will die at the place you go to second. It's up to you to choose who will be on the potential death roster.
You can control who it is who dies as the person you are closest/furthest to will perish if they are at the location you visit second. For example: I stayed to defend the Lodge while Andreja (my wife in-game) was on The Eye. After going back there, she didn't make it. However when I replayed and instead went to The Eye first, I found Sarah, with whom I had the poorest relationship, dead at the Lodge.
I encountered a nasty bug when trying to fly from The Eye back to the Lodge where all landing points in New Atlantis were blocked out. The quick fix is to warp away to another system and then warp back and the bug should go away (just make sure to unload your contraband before returning, as I failed to do.
"But officer, my teammate could have used those harvested organs.")