It is recommended to get two pairs of Feather Boots, but not equip the Auto-Float support ability that goes with them. The Feather Boots absorb Earth damage, so one will be healed when the Earth Guardian uses Earth Shake. During battle, it is possible to use Quina's Eat/Cook command to learn Guardian's Earth Shake as Blue Magic. He is the only boss who can be eaten.
If Quina has Mighty Guard, the battle can be won with ease. Another good idea is equip Auto-Regen and Auto-Haste. As the Earth Guardian is a flying monster, Twister can help out greatly. Zidane should do the damage with his physical attacks. If Quina knows Bad Breath the battle becomes even easier, since Earth Guardian is weak to Darkness and Mini. Aqua Breath will inflict above 4000 HP in one use. Zidane's Demon Killer support ability can make the fight easier still.