SPECTRAL KEEPER -- HP: 52000 -- AP: 12000
First tip... try make sure you have all your Overdrives full (Aeons too).
You can use the Trigger Commands to reposition your fighters on any of the available 6 fields. Haste will be very useful in this battle. Your opponent generally uses attacks which cause Berserk, if you have any Berserk protection, make sure you equip it before the fight, if not make sure you have some Remedy or have learnt Esuna.
If you attack, the Spectral Keeper will counter by attacking the 3 fields infront of him, it is therefor important to position the charecter with the most HP and the greatest protection (using the spell protect will be very useful) infront of the creature with 2 other fighters behind the Spectral Keeper. If you put all your players behind him, he will simply turn around which could prove very nasty. Your best bet is to leave a field free between your charecters, you can then use provoke to make sure the charecter with the most HP (infront of him) gets attacked.
Your opponent will occasionally use Glyph Mines on 2 of the 6 fields. These will explode after a number of turns instantly causing death, don't waste any time moving your fighters to saftey. If you summon an Aeon, the poor creature will instantly fall victim to the mine but it is a worthy sacrifice. Since Aeons cannot last long against the Spectral Keeper, your best bet is to use an Aeons Overdrive immedietly. Incidentaly, there is no point selecting Dismiss as your charecters will simply be blown up by the Glyph Mine intended for the Aeon.
Save your game after defeating your opponent, it might be a good idea to then leave the temple and fill your Overdrive gagues (Aeons too if possible) as things are about to get tricky..