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