Here is the full list of all 15 Purrs in Heaven achievements.
Complete World 1
Complete World 2
Complete World 3
Finish the game
Collect 50 coins
Collect 20 fish
Make a purchase in the store for the first time
Make 4 purchases in the store
Get your first cartridge
Complete the minigame without failing
Die 50 times
Defeat 20 enemies
Make Petrus angry
Talk to Yama 5 times
Complete the sky map