In the end, you're looking to defeat the monsters and come out with the most trophies.
From the campaign:
The Guardians: Explore is a strategic deck refinement game for up to four players, where you fight monsters, sometimes cooperatively, for trophies. The game takes place over two game chapters. In the first chapter, the warm up, you choose thirteen guardian cards to supplement your seven generic cards. These will drive your strategy for the second game chapter. If this is your first time playing there are preconstructed sets of thirteen guardian cards for you to learn with! In the second chapter, the battle, you have four individual turns and two cooperative turns to acquire as many trophies as possible and claim the title of true guardian.