Here is the full list of all 27 NYAN DESTROYER achievements.
Destroy 30 mother cat's
Destroy 30 kittens
Destroy 20 poodles
Destroy 50 dogs
Destroy 30 cats
Destroy 30 of some brown enemies
Destroy 30 pumpkins
Destroy 30 donuts
Destroy 30 "Deal With Cats"
Destroy 30 Pinatas
Destroy 150 metiorites
Destroy 5 witches
Destroy 15 aggressive cats
Collect 1000 coins
Buy all ships
Complete 10 games
Collect 10 bonuses
Collect HP
End the last stage
Complete the battle by playing for "Heart"
Complete the battle by playing for "Guitar"
Complete the battle by playing for "Watermelon"
Complete the battle by playing for "Pizza"
Complete the battle by playing for "Spinner"
Complete the battle by playing for "Something triangular"
Complete the battle by playing for "bow-tie"
Complete the battle by playing for "Butterfly"