One of the harder achievements I've tried to get and this achievement IS NOT FUN. I got to day 49 and lost due to a bad beginning. The video below is great! but make a cookhouse BEFORE day 3. This will remove the "no raw food" issue you will start to have and gives you a 2 day grace period before you need to send out hunters.
There are 3 "versions" of the map you select. These change the location of every resource on the map.
Keep resetting till you get this exact map on "carter". Don't go for any other achievement while you are going for this one.
Here is a "walkthrough" video that also gives some useful tips. Follow this EXACTLY. Sick people are random in this hard mode, so if your's is well above her's just load a previous save: