Fafnir is a real bastard in my opinion. Do you have the Genji Equipment? I know a good strategy and it works better with the Genji gloves.

You'll basically need a rank (I chose Basch) give them the best Samurai sword you have (Beat "Ancient Man of Mystery" and you get the Masamune as the reward.) You'll want to berzerk and haste this character and they will become a combo monster dealing 6-12 hits doing anywhere from 5000 to 9999 points of damage.

Build a similiar "magic" based character using Flare to nail him while he switches immunity. Your third character should be your healer and try to stay away from the group so you don't get caught up in his mega spells. Make sure your casters are using shields so you can block attacks and reduce your damage.

Alternate between attacking and healing. It also helps to bring in a second string team into the beginning of the fight te remove his status buffs and to use quickenings on, that way your main party will have less to deal with. Also be careful, he tends to sneak in status buffs throughout the battle so you need to dispel them quickly so you are constantly doing max damage.