The Guardian runs out several battle programs to determine its attacks:
Air Force Battle Program : Diffractive Laser, Launcher, Magitek Laser, Wave Cannon (including a countdown)
Dadaluma Battle Program : Ashura, Hi-Potion, Magitek Barrier, Mythril Knife, Potion, Shockwave
Default Battle Program : Atomic Rays, Magitek Laser, Missile
Ultima Battle Program : Flare, Flare Star, Meteor, Ultima
Ultros Battle Program : Ink, Entwine, Stone, Tentacle Begin with a self-Hastega and an enemy Slowga. Toss up Mighty Guard if you can, and Reraise is always a cool idea. On offense, focus on Thundaga, Ramuh, Lightning Scrolls, Throwing other Thunder/Lightning crap, Valigarmanda, Bahamut, Flood, Leviathan, etc. Not too much to say except the faster you go, the better.
Once you're done, use the nearby Save Point. Use a Tent there and Save. Then go north into the next area. There, go west and south through the door. Back outside, go north and heal up. Continue to the statue for another fight...