Genais does most of the fighting here, and while it is alive the Core is out of range. When Genais withdraws into its shell, the Core will charge energy and use Gravija on the party, while Genais uses Sigh to damage the party and inflict Darkness. Once Genais is slain, the core's only attack is Gravija, and thus it is easily destroyed. When attacked, the Core will counter with a low-level Black Magic spell on the party, so there is a slim chance it can kill a party member. As long as the player heals, the risk is minimal.