this achievement is one of the mostly working ones in this mode. all you need to do is survive for 7 days, however if you reach "freezing" or "starving" when your warmth/hunger drops too far, you will fail the challenge. this seems to be a glitch.
make sure you select this challenge, Nature Retreat. i usually pick the cards that give food from killing and looting enemies, double food from small animals, and the baba yaga outfit that gives all skills. then my last one is usually something like Deep Pockets or whatever that loot starter pack card is.
start out by getting the items from the snowcat, and as many sticks, and anything else, as you can find around the beginning area. your main goal is to find either a burning barrel or a house with a black woodstove. those will always stay warm and you can just basically stand near them the whole game until you get hungry.
your hunger meter goes to a full green circle, then a green bar halfway around the circle when at max. the half circle lasts 5 minutes, afterwards you will stay at full green for a minute before it goes down a tick every 10 seconds. a day lasts 6 min and night lasts for 4, so you can easily go half a day on full food. usually what i do is just kill a small animal whenever my bar gets to a quarter circle (2.5 min). with the double food card this will give you another quarter circle of food, back to max.
as long as you have enough ammo to continue killing animals for food you should have no problem surviving for 7 days. you may get lucky and have a bird spawn point near you. that gives unlimited feathers to help make more arrows. if you go exploring from your "home base" fire, be careful as it's very easy to get lost without a map, and the markers only last until you are so far away. the achievement should pop up as soon as the 8th day starts.