For this achievement all you have to do is beat all 5 stages for the first time. This is actually almost impossible to miss. No matter how many bombs or Ninja Stars you hit you can not fail the game. Just keep slashing at those pizza boxes and statues until it pops. Each level lasts only 2-3 minutes and once you have finished the Leonardo level this achievement will be yours.
Level 1: Training
Level 2: Donatello
Level 3: Michelangelo
Level 4: Raphael
Level 5: Leonardo