Here is the full list of all 20 Timberman achievements.
Score 1001 or chop 150000
Score 700 or chop 100000
Unlock at least 4 out of 5 new steam exclusive characters
Beat 10 much stronger opponents in multiplayer
Defeat 5 different people in multiplayer
Win three rounds in a row by being much faster than opponent
Win 33 4 players matches
Fight 10 times in multiplayer mode
Defeat 25 people by being much faster in 4 players mode
Fight in multiplayer with devils and angles only
score 555 or chop 55555
Score 500 or chop 30000
Score more than 200 three times in a row
Let yourself be killed by branch with score 180 points exactly
chop 100 logs in 15 seconds
Launch the game 9 times
Score 250 or chop 3917
Chop 200 logs in over 46 seconds in a single player game
Score 150 or chop 1117
Chop 10 logs in 2 seconds