Here is the full list of all 13 Herding Dog achievements.
You are as fast as the Flash
Travel 1000 meters
Accomplish your first dog mission
Traveled 100 meters
Traveled 50 meters
More than 50% of success protecting animals
Save rate more than 5%
Combo rate more than 60%
10 missions completed
Achieved more than 50% zen state
Visit all the world zones
Flexibility rate more than 10%
Fight rate more than 5%