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