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