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