Any magic that is directed at the Core will be absorbed by Genais, so it is important to dispose of it first. Unlike the similar-looking Sinspawn Geneaux, Genais begins the battle outside its shell, but like Geneaux, the full brunt of physical attacks as well as lots of Fire can be used to weaken it. Genais will use Poison-based attacks and counter any magic with Waterga.
Once its HP drops past 50%, it will retreat into the shell and begin casting Cura on itself as a counter to any attacks. While Genais is inside its shell, the Core will charge and unleash the powerful Gravija, which is very harmful to the entire party. Summoning an aeon and using its Shield ability will negate most of the damage.