Here is the full list of all 33 Lumberjack's Dynasty achievements.
Have a kid
Exceed 1,000,000 Social Points
Own 25 forests
Own 1,000,000 Euro
Catch 500 fish
Max out all the skills
Catch 50 fish
Plant 500 trees
Cut down 500 trees
Exceed 100 km/h in a vehicle
Find 30 treasure chests
Rebuild special community buildings
Learn all possible recipes including unique ones
Expose dirty truths and become a Mayor yourself
Stand side by side with Mayor and become his deputy
Help James with all his resort buildings
Plant 50 trees
Own 10 vehicles
Own the farm and lumber mill
Own a furniture factory
Marry a beautiful woman
Own 5 forests
Create 100 wood plank pallets
Learn recipes from all the cook books
Help 50 people
Cut down 50 trees
Help 25 people
Own over 20 animals total
Own 5 vehicles
Repair all of the lumber mill buildings
Repair all of your farm buildings
Help 10 people
Own a tractor