Heres the rundown for farming Briareus.
The pop items are as follows: Dented Gigas Shield (Adamastor), Warped Gigas Armband (Pentagruel), Severed Gigas Collar (Grandgousier)
These Key Items are also farmable from Gold Pryxis in Abyssea - La Theine Plateau
Drops: Helm of Briareus - X, Briareus' Sash - O, Jewel of Vayage - O (Whm, Thf, Brd, Sam Pup) +2 feet upgrade, Stone of Voyage - O (War, Rdm, Pld, Smn, Dnc) +2 feet upgrade, Hakke Hackimaki - O, Imnicus Cuisses - O
Atma: Atma of the Stout Arm - Str +40 , Attack +50 , Ranged Attack +Major