You will unlock this achievement early on in the game. You will need to land the first colonists on Mars and have at least one of them survive for ten sols. Make sure to have some basic knowledge about the game by playing through all the tutorials.
Next up is to build a dome. For instructions on how to build a dome follow my guide for this achievement:
Next you want to call in a rocket of colonists and build housing and a grocer in your dome. Also make sure to start some food production detailed in my other guide:
When the colonists arrive you will need to keep them alive for 10 sols. Make sure to keep the dome supplied with water and oxygen so that your colonists don't die. Food production should produce you enough food to keep your population alive and happy. You can end the Colony Approval stage early if you manage your colonists to have a baby and also unlock this achievement:
After 10 sols or after having a baby born you will receive a notification and unlock the achievement.