It has been a while since I defeated Geosganeo but I don't think its too hard. I hope you have worked on building up Tidus, Rikku and Wakka as they're the only ones who can fight underwater. Equip death and petrification armour to your characters and cast haste. Have your characters overdrives full and he won't last long. Grenades are also helpful. Geosgaeno only has about 32000 hp.
Do you know that to obtain Anima you have to have the bonus items from the six temples in Spira?
Good luck!