Pretty much the same way anybody kills anything on Blue Mage. The first step is to figure out which moves you really need or want to Stun by looking at a wiki entry if you don't already have that in mind.
Sudden Lunge is the only truly vital spell, Triple Attack and Dual Wield III are the only truly vital traits. Spells that critical will do solid damage since Briareus Gigaspants lives in a ????apple under Abyssea-LaTheine. If needed, Auroral Drape and a hybrid evasion set help immensely to reduce the damage output of just about anything in the earlier Abyssea zones.
How fast you can kill Briareus compared to how safe you'll need to be will depend on whether you're solo or with a healer. Also a vital determinant, how much lead-based paint that healer drinks each morning.
Good luck with, I assume, your Almace!
