Here is the full list of all 18 Lock Lock: Farm achievements.
Take the first star
Complete the first level
First stage with three stars
Complete 5 levels
Complete 10 levels
Complete 15 levels
Complete 20 levels
Complete 30 levels
Complete 25 levels
Complete 35 levels
Complete 40 levels
Complete 45 levels
Complete 50 levels
Get 10 stars
Get 150 stars
Get to catch 3 types of animals
Catch 7 types of animals
Catch 12 types of animals