Here is the full list of all 39 TY the Tasmanian Tiger achievements. It takes around 12-15 hours to unlock all of the achievements on Windows.
Run out of lives. So sad...
Defeat 200 enemies using your Bite
Set a best time with the Chronorang equipped.
You didn't miss with a single boulder!
You found all the Picture Frames!
You got 100% of everything!
Defeat 75 enemies with the Zappyrang
Hit Shazza with the Flamerang
Burn 50 Cricket Bats
You got all the Rainbow Scales
You got the Chronorang
Get all the boomerangs
Completed All Time Attacks
You found all the opals!
You found all the Bilbies!
You got the Kaboomerang
Hit Lenny with the Flamerang 15 times
You got the Megarang
Defeat 100 enemies with the Flamerang
You got the Infrarang
Get a thunderegg from a turkey using a super bite
You got the Multirang
You learnt how to swim!
You got the Zoomerang
Bite a leech.
You got your second rang!
You got 100% of everything! (HardCore)