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