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