You will unlock this achievement by getting the companion (dog) Pancake to join your shelter.
For his questline, you will need (1) A flashlight (2) One can of food (3) A map/Axe (4) A med kit.
The first pop up will mention growling and glowing eyes. Just make sure to use the flashlight here to not kill Pancake. The rest of his missions will mention specifically that it is for him.
Do not get Sharikov by trading a man with a bag a Soup Can or the other pop ups mentioning allowing a cat to enter your bunker. This will stop Pancake from entering^Doing this after Pancake enters your home will make Pancake leave, unlocking:
(Though Pancake is the preferable choice otherwise)