The Greater Sphere is vulnerable to an element, but shifts it randomly once hit by its weakness. Unlike the Spherimorph, the Greater Sphere absorbs any other element. After the Greater Sphere attacks with an elemental attack, it will be weak to that attack's opposite element.
It will counter all normal attacks with Ultima. On its turn it will alternate between a normal attack and unleashing Hydraulic Press, which deals fractional damage to the party, equal to 15/16 of each character's maximum HP. For every Overdrive the Greater Sphere survives it will counter with Hydraulic Press. The damage from Hydraulic Press can be reduced using Protect and Defend.
The Greater Sphere is unusually time consuming to defeat and very powerful. Auto-abilities, such as Break HP Limit, Auto-Haste, Auto-Protect, and Auto-Shell, prove helpful, and a high Magic Defense attribute is vital. Before attacking Greater Sphere, the player should be prepared to weather its Ultima counterattack.
When farming Greater Sphere for Luck Spheres, the player will want to kill it as fast as possible. The fastest strategy is to use Tidus's and Wakka's Overdrives, Slice & Dice (if successful) and Attack Reels with 12-hits respectively (both once), to defeat it quickly. Using Auto-Life will make this strategy easier.
Another helpful strategy is to summon Anima and cast Protect and Haste. If Anima loses health, she should cast Curaga. She should use Oblivion when it becomes available. If Oblivion doesn't finish Greater Sphere, Anima may suffer damage from Hydraulic Press up to three times (which might end up killing her). This strategy is only viable in the International/PAL/HD versions.