The Boss Gobby will order the Minion Gobbies to attack physically, but will do minimal damage if the party is in the back row. Otherwise, Boss Gobby will not attack otherwise unless attacked. If he is attacked, he will counter with Black Magic like Thundara, Bio, or Firaga, both cast on the entire party. Firaga will do over 1000 damage and may kill Rydia if she is at a low level. Bio and Thundara do much less damage. If the Minion Gobbies are killed, Boss Gobby will use Protect, Shell, Haste, and Curaja on himself, then begin attacking physically, doing much more damage than the Minion Gobbies, and regularly uses Curaja again.
If Rydia is at a high enough level to use Bio herself, during a Full Moon Bio will do enough damage to kill the Boss Gobby in two casts, though if he counters the first Bio with Firaga Rydia will likely need to be revived and healed. Alternatively the player can put both Luca and Rydia in the back row and kill off the Minion Gobbies, then have Rydia use Bio while Luca uses Big Throw - the Boss Gobby's Curajas after his initial round of buffs will not heal much damage and Rydia and Luca can outdamage the amount he recovers easily. Plenty of Hi-Potions should be brought for recovery.