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