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