As you leave the druid grove and move west, you'll come across a white dog with a slain owner. SAVE. Pass an animal handling or charisma check to add the dog to your camp. Reload if you fail, it's not a hard check.
After a few nights, the dog will bring you a ball. Pass a animal handling, sleight of hand, or deception check to take the ball into your inventory. Leave the conversation. Use the throw command in the hot bar to throw the ball. Scratch will grab it and bring it back. Take it again to earn the achievement. You'll have lots of chances for this part if you fail. You can also pick up or buy a ball in many places.