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