Successfully complete the indicated quest to unlock an item that allows you to summon the listed Esper when you have a full Smash Gauge:

Adrammelech: The Moorabella Cup
Belias: The Camoa Cup
Hashmal: The Fluorgis Cup
Mateus: The Graszton Cup
Shemhazai: Of A Feather
Ultima: Hunted
Zalera: The Last Step
Zeromus: The Five Kings