During the main story, you will eventually find yourself in an area called Shipping and Recieving, with a quest of the same name. You'll find a group of survivors huddled around a large door with many enemies on the other side. You need to open the door and kill all the enemies without a single person being killed.
This might look difficult at first, but its actually pretty straightforward; unless you hack the door open, you're going to be asked to find a turret fabrication plan and then secure the door with some turrets. You'll need two turrets deployed and pointed at the door to gain the trust of the character with the door code. In order to prevent anyone from dying, just go above and beyond with the door defense. More turrets means an easier achievement!
For a guaranteed win (tested it several times, to be sure I wasn't just getting lucky!) use five turrets. You can find several of them lying around the area, and fabricate another two. Make sure the turrets are all hacked if you have too many alien neuromods, and have all of them fortified. When you open the doors, get ready with a psyshock or a nullwave transmitter and use either on the weaver. The turrets will take care of the rest with no issue.