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