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