Here is the full list of all 31 Ultimate Chicken Horse achievements. It takes around 15-20 hours to unlock all of the achievements on Windows.
Die with the coin 10 times
Win without any special points
Unlock a level
Play 10 games
Play 30 games
Play 100 games
Play 10 games online
Play 50 games online
Play online with a local friend
Place 200 traps
Place 1000 traps
Unlock all levels
Unlock a character
Unlock all characters
Unlock an outfit
Unlock all outfits
Fall into the void 100 times
Kill people with traps 100 times
Kill someone with an arrow 100 times
Kill someone with a hockey puck shooter 100 times
Die on barbed wire 10 times
Wall jump 1000 times
Attach two blocks together with glue
Glue four blocks together
Get 10 post-mortem points
Teleport 50 times
Enter sudden death 20 times
Get 50 coins
Score 50 comeback points
Score 100 solo points
Die 50 times in a black hole