Kuja casts Thundaga and Demi frequently and will only use the special Flare Star magic if party members are under the Reflect status, or if he is attacked by an ability that lowers his MP. Flare Star is a devastating spell damaging the whole party that neither Shell nor Reflect can protect against.
Successfully depleting his HP will cause Kuja to enter Trance form and cast Ultima, putting an end to the battle.
The damage inflicted by Thundaga and Demi is easily cured by a casting of Cura or Curaga. Equipping the Coral Ring makes characters absorb Thundaga. It is not advised to trigger Kuja to use Flare Star by using Reflect or attacking his MP; characters with Auto-Reflect equipped will cause him to use Flare Star.