If the Core is attacked while the Sand Golem is still animate, the Golem will counterattack with a harsh physical strike. The Core will eventually resurrect the Sand Golem, starting the process over again. Other than this revival move, the Core has no other attacks. Defeating the Sand Golem multiple times is not enough; the Core must be destroyed to end the battle.
It is best to deal enough damage to the Sand Golem to immobilize it before attacking the Core. Vivi's Ice magic is good.