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