Aside from the completion rewards you’ll get by playing Adventure mode, the total number of stars you collect from each stage will count towards your Star Collection list. In the lower left corner of the adventure map screen, you’ll see the Star Collection reward list.
Keep playing adventure more and clear individual stages with 3 stars. Don’t worry if you’re able to secure 1 or 2 stars; you can always repeat those stages later on once you have a more powerful team to make it easier to gain 3 stars. Stars are affected primarily by the number of surviving members of your party. In Normal and Hard mode, it is imperative to go switch to Manual Mode when dealing with bosses to increase the survivability of your team.