Compiled by me with reference to several walkthroughs.

Disc 1

G.F Name				Elemental		Found at		Attack
		Quezacotl		Thunder		Tutorial desk		Thunder Storm
		Shiva		Ice		Tutorial desk		Diamond Dust
		Ifrit		Fire		Fire Cavern		Hellfire
		Siren		None		Draw from Elvoret (Boss) at Dollet Communications Tower		Silent Force
		Brothers		Earth		Tomb of the Unknown King (defeat the Brothers)		Brotherly Love
		Diablos		None		Magical Lamp from Cid (defeat Diablos)		Dark Messenger
		Carbuncle		None		Draw from Iguions (Boss)		Ruby Light (casts reflect)

Disc 2

G.F Name				Elemental		Found at		Attack
		Leviathan		Water		Draw from NORG (Boss) at Balamb Garden		Tsunami
		Pandemona		Wind		Fujin and Rajin (Boss)		Tornado Zone
		Cerberus		None		Main Hall of Galbadia Garden		Counter Rockets (casts Double & Triple)
		Alexander		Holy		Draw from Edea (Boss) in Galbadia Garden		Holy Judgment (drives elemental weakness onto enemy

Disc 3

G.F Name				Elemental		Found at		Attack
		Doomtrain		Poison		Requires Solomon Ring at Tear's Pt. in Esthar plus additional items		Runaway Train
		Bahamut		None		Deep Sea Research Center in SW corner of world. Must answer some questions correctly		Mega Flare

Late in Game

G.F Name				Elemental		Found at		Attack
		Jumbo Cactuar		None		Cactuar Island		1000 Needles
		Tonberry King		None		Defeat a certain no. of Tonberrys at Central Ruins, then defeat Tonberry King		Chef's Knife
		Eden		None		Defeat Bahamut at Deep Sea Research Center. Head underwater, encounter Ultima Weapon then draw from it.		Eternal Breath