Thankfully they didn't require any additional purchases for this game. For that matter, there's no Arena or Nightmare Mode achievements either. Unless you have a desire to play on a higher difficulty, there's no reason to play on anything other than Beginner.
Stars are broken into 3 parts. Story Goals (unmissible), Collections (Chests, Soul Gems, Frames) and Dares (Gongs, Find All Areas, Speed Run, etc)
There are 10 story levels that grant progress toward this achievement. On top of the story levels are expansion pack levels as well as one special level on the M.A.P. for each different elemental Sensei. Each level can grant 3 stars.
Simply completing the story itself with little exploration or attention to collectibles will grant you 10 stars. The Starter Pack comes with 2 different Sensei's (Golden Queen is Earth element and King Pen is Water element) and their levels on the MAP are quite short and simple. You will easily get all 3 stars from both of the available Sensei levels. That leaves you with only 4 more stars to get.
Of note, Fizzland and The Golden Arcade do not have a Speed Runs so you can take your time and explore (or use a guide) to find everything for all 3 stars.
If you are looking for a good guide for the game, I suggest:
darkSpyro