Challenges pop naturally throughout the course of the game through various actions. Just playing the first 30 minutes would net you this achievement. The notification for completing a challenge appears on the lower left side of the screen. You can access the challenge menu by going to start to open up the map, LB to open next menu and selecting Challenges. The challenges are really easy for the basic tiers.
Examples are:
Reach level 4,6,8
Equip a perk card
Collect a bobble head, holotape or magazine
Collect wood
Harvest plants
Scrap junk
Deploy a C.A.M.P
Cook a meal
Boil water
Acquire a disease
Kill a creature
Kill an enemy
Repair a piece of armour or weapon
Destroy a robot