Disney Infinity

tl;dr version: Just play the game and it'll eventually pop.

I desire a verbose, detailed explanation for my achievements version:
For this, you need to get 70 stars across the playsets for Monsters University, Pirates of the Caribbean, and The Incredibles and in the Toy Box. Add-on Playsets such as the Lone Ranger or Cars will not count for this.

To earn Stars in Play sets, you must complete specific missions. To find what missions to complete, simply bring up your mission log and hit right on your control stick. You should see a list of Gold Star Missions. Completing each of these nets you a star. Ones you have completed will have a star next to them.
One thing to note for the completionists: Some of the Gold Star Missions are character specific, and will require you to have extra characters (For instance, each of the Incredibles characters have specific training missions that will award gold stars to each of them.).

To earn stars in Toy Box mode, you can either level up your characters, or complete adventures. To get the stars for characters, visit their statue in the hall of heroes. For each grade of statue (Bronze, Silver, Gold), you'll get one star. For adventures, you need to earn medals. Each medal you earn equals 1 star.
NOTE: While the extra playsets do not count, the characters do. Upgrading extra characters or medaling in their specific missions will count towards your total.

Honestly though, you really don't need to go out of your way to get this if you're going for the other achievements. As if you play through each of the play sets and get 15 stars apiece, then play adventures to get 18 total medals, that will put you at 63 stars. Also, by then, assuming you used one character the whole time through each play set, your characters would have leveled enough to get 3 silver statues bringing your total up to 69, leaving you with 1 star to get.