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