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