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