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