Here is the full list of all 24 Farmer's Dynasty achievements.
Own a tractor
Fix 1 building
Have 1 field plowed, cultivated and sown
Welcome to your new farm!
Fix 10 buildings
Fix 100 buildings
Own a tractor, plough, cultivator, seeder, trailer and a combine
Own full set of modern (not old) machines
Renew all your farm buildings
Have 4 fields plowed, cultivated and sown
Have 10 fields plowed, cultivated and sown
Drive 100 km
Get married
Have a child
Own 10 fields
Have a child at school
Help 10 people
Help 20 people
Help 50 people
Own 250,000 Eur
Own 1,000,000 social points
Catch 100 fish
Own 10 animals
Find and open 30 treasure chests