There is a one-in-three chance that Oblitzerator will counter with a barrage of blitzballs. For physical attacks, the counter causes Darkness; for magic, they cause Silence. Tidus should cast Cheer for his and Kimahri's strength, and use Haste on Lulu so she can unleash many Thunder spells. Lulu should use Focus a couple of times to ensure the Overkill. On its turn, Oblitzerator will use Blitzball Rush, which randomly hits the whole party for high damage.
With 6,000 HP, Oblitzerator is a difficult battle, especially since its Agility will increase with every turn and Yuna is not available to heal the party or call an aeon. However, an option becomes available where Tidus will notice a crane on the deck, which needs to be hit with Thunder three times before Tidus can use the Trigger Commands to activate it and remove Oblitzerator's top half, effectively weakening and lowering his HP to 1/16th (a maximum of 375). The fight will not last much longer after that.