You need to earn all 225 stars across the 75 levels in the game. Stars are entirely related to score, with higher scores earning you more stars, up to three per level. The score requirements for the stars are visible when you first click on the level to play. The requirements are lower for the earlier worlds, and get harder as you progress to the later worlds, and through each individual world. You will certainly have to use monsters with good boosts to be able to three-star some of the tougher levels of the game where you are required to get more than 2 million score. Being able to afford using these monsters so frequently may require some boosting of coins.
Earning all 45 stars in a single world will earn you the "Shooting Sugar Stars" achievement along the process.