Here is the full list of all 27 Jack Lumber achievements.
Spend 100000 Logs in the store. (Lifetime)
Use 100 Syrups
Finish all of your errands like a good lumberjack.
Buy all the beards
Get a gold sash for every animal
Buy five pictures for your cabin.
Get a silver sash for every animal
Use 50 Syrups
Spend 50000 Logs in the store. (Lifetime)
Own at least one of every syrup at once.
Learn the names of the people that made this game
Re-watch a cutscene
Hit 10 animals
Use 15 Syrups
Beat a level with three or more beards on.
Get a bronze sash for every animal
Beat World 4
Beat World 3
Read all of the letters from Ranger Bob
Read all of the letters from Jill Timber
Beat World 2
Click the animals in the Cabin 200 times.
Beat a level with one or more beards on.
Spend 5000 Logs in the store. (Lifetime)
Beat World 1
Get a painting for for Jack's cabin
Get a plaid sash for every animal