Here is the full list of all 13 Herding Dog achievements.
You are as fast as the Flash
Travel 1000 meters
Fight rate more than 5%
Traveled 100 meters
Accomplish your first dog mission
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%