This trophy is called Searcher. You need to get all the Ansem reports
Ansem Report 1: Defeat Jafar Genie in Agrabah.
Ansem Report 2: Received Once you seal the Hollow Bastion Keyhole
Ansem Report 3: Defeat Ursula in Atlantica.
Ansem Report 4: Receive from Aerith in the Hollow Bastion Library after sealing the keyhole to that world.
Ansem Report 5: Defeat Maleficent in Hollow Bastion.
Ansem Report 6: Receive from Aerith in the Hollow Bastion Library after sealing the keyhole to that world.
Ansem Report 7: Defeat Oogie Boogie in Halloween Town.
Ansem Report 8: Defeat Hades in Olympus Coliseum (during the Hades Cup).
Ansem Report 9: Defeat Captain Hook in Neverland.
Ansem Report 10: Recieve from Aerith in the Hollow Bastion Library after sealing the keyhole to that world.
Ansem Report 11: Defeat the optional boss Kurt Zisa in Agrabah.
Ansem Report 12: Defeat the optional boss Sephiroth in Olympus Coliseum.
Ansem Report 13: Defeat the optional boss Unknown at Hollow Bastion.