Take on Sphinxaur first. Junction ice magic to Elem-Def. Unlock GFs.
Take on Tri-Point Second. Junction thunder magic to Elem-Def. Unlock Magic.
Take on Krysta next. It counters most attacks. High level Diablos and Cactuar attacks work well. I'd unlock Resurrection at this point.
Trauma should be taken on next. Pandemonia and wind magic work on it. Unlocking Limit Breaks is useful. If you rely heavily on them, unlock them earlier.
Next up is Red Giant. It relies on physical attacks so blind it. Magic or GF's work better than physical attacks. I'd unlock Item by now.
Garguntua uses earth magic and beserk, so junctionto your Stat-Def and Elem-Def accordingly. Unlock Command Ability next.
Catopas uses thunder attacks so junction thunder magic to Elem-Def. Unlock Draw.
Tiamat is slow to attack. Avoid using fire thunder and wind magic. Unlock Save (since you can always leave the castle to save)
Omega Weapon stategies are covered in other threads.
http://www.eyesonff.com/forums/showthread.php?t=60849
EDIT: Ultima Shadow, good point about Draw. But if you have a full roster of GFs it's a low priority.