The following is a list and description for each of the GFs in the game.
Note:The Hp and damage shown is it without using the SumMag+ and GFHp+ abilities [or using Boost].

Select a GF to learn about:
Quezacotl
Shiva
Ifrit
Siren
Brothers
Diablos
Carbuncle
Leviathan
Pandemona
Cerberus
Alexander
Doomtrain
Bahamut
Jumbo Cactaur
Tonberry King
Eden

Quezacotl          Element: Thunder "Thunder Storm" [All]
Name From:Aztec Mythology [Thunder god]
Starting Level:1        Hp:300        Damage:275
Level 100        Hp:5650    Damage:3542
Best skills: Elem Def x2, Card, T-Mag RF, Mid Mag RF
How to get: Access Squall's study panel. [Disc 1-3]

Shiva              Element: Ice "Diamond Dust" [All]
Name From:Native American Mythology [Moon/ Ice godess]
Starting Level:1        Hp:298        Damage:263
Level 100        Hp:5450    Damage:3563
Best skills: Elem Def x2, Doom, I-Mag RF
How to get:Access squall's study panel. [Disc 1-3]

Ifrit              Element: Fire "Hel Fire" [All]
Name From:Middle Eatern Mythology [Demon spirits "efreeties"]
Starting Level:1        Hp:305        Damage:298
Level 100        Hp:6150    Damage:3695
Best skills:Elem Defx2, Mad Rush, F-Mag RF, Ammo RF, Str Bonus
How to get: Defeat in the Fire Cavern [Disc 1]

Siren              Element: None [Silence] "Silent Voice" [All]
Name From: Irish Mythology [Female banshees]
Starting Level:3        Hp:391        Damage:223
Level 100        Hp:5350    Damage:2559
Best skills: ST Atk-J, ST Def-J x2, Treatment, Mag Bonus, L-Mag RF
How to get: Draw from Elvoret [Disc 1] or Tri- Point [Disc 4]

Brothers[Minotar/Sacred]Element: Earth "Brotherly Love" [All]  
Name From: Greek Mythology [Minataur = Half bull]
Starting Level:7        Hp:670        Damage:529
Level 100        Hp;6350    Damage:3737
Best skills: Defend, Cover, Hp Bonus
How to get: Defeat in Tomb of The Unknown King [Disc 1-4]

Diablos              Element: None [Gravity] "Dark Messenger" [All]
Name From: Spanish Mythology [Spanish for Demon]
Starting Level:9        Hp:730        Damage:9% of target's Max Hp
Level 100        Hp:5950    Damage:100% of target's Hp
Best skills: Ability x3, Darkside, Mug, Enc-None, Time Mag RF, ST MagRF
How to get: Speak with Cid before going to Timber to get the Magical Lamp, use it to summon him. You must then defeat him. [Get Lamp in Disc 1]
Note: Regaurdless od Diablos'  Level, he can only do up to 9999 damage.

Carbuncle          Element: None [Reflect] "Ruby Light" [All]
Name From: Unknown
Starting Level:16        Hp:1220    Damage:NA
Level 100        Hp:6650    Damage:NA
Best skills:ST Def-J X2, Ability X3, Vit Bonus, Counter, Recov Med RF
How to get:Draw from Iguions [Disc 1] or Krysta [Disc 4].

Leviathan          Element: Water "T'sunami" [All]
Name From: European Mythology [Sea serpents]
Starting Level: 17    Hp:1349    Damage:963
Level 100        Hp;7050    Damage:4036
Best skills: Elem Def-J X2, Recover, Spr Bonus, Auto Potion, Supt Mag RF
How to get: Draw from NORG [Disc 2] or Trauma [Disc 4].

Pandemona          Element:Wind "Tornado Zone" [All]
Name From:Unknown
Satrting Level: 19    Hp:1442    Damage:1052
Level 100        Hp:6850    Damage:4082
Best skills: Elem Def-J X2, Absorb, Initiative
How to get:Draw from Fujin [Disc 2] or from Red Giant [Disc 4].

Cerberus          Element: None [Triple] "Counter Rockets" [All]
Name From: Greek Mythology [Dog that guards the underworld]
Starting Level: 23     Hp:1490     Damage:NA
Level 100        Hp:5950    Damage:NA
Best skills: ST Def-J X4, Ability X3, Auto Haste, Expend X2-1, Alert
How to get: Defeat it in Galbadia Gardens [Disc 2] or draw it from Gargantua [Disc 4].

Alexander          Element:Holy "Holy Judgement" [All]
Name From: History [King of England, "Alexander The Great"]
Starting Level:25        Hp:1925    Damage:1350
Level 100        Hp:7250    Damage:4188
Best skills: Elem Def X4, Ability X3, Revive, Med Data, Hi Mag RF
How to get: Draw from Edea [Disc 2] or from Catoblepas [Disc 4]

Doomtrain          Element:Poison [Status] "Runaway Train" [All]
Name From:Unknown
Starting Level: 28    Hp:2521    Damage:1931
Level 100        Hp:8650    Damage:5396
Best skills:ST Def-J X4,Darkside,Absorb,AutoShell, JunkShop,ForbMedRF
How to get:Get the Solomon Ring at Tear's Point near Esthar, and get six Malboro tentacles, Remedy +, and Steel Pipes, then use the ring.

Bahamut          Element:None "Megaflre' [All]
Name From:Unknown
Starting Level: 35    Hp:3274    Damage:1451
Level 100        Hp:9150    Damage:3571
Best skills:Mug,MoveHpUp, Autoprotect,Expend 2-1,RareItem,ForbMagRF
How to get: With the Ragnarok go to the Deep sea research center near the bottom left corner of the map [it doesn't appear on the map, though]. Init you'll find a huge glowing core.  Encounter None doesn't work in here. See how the core glows then fades? walk only when it's fading to avoid enemy battles. When you reach it, press the comand button.  He'll ask you 3 questions.  Question 1, choose the top answer. Question 2, Choose the bottom, Question 3, choose the third one which is hidden under the 2nd.
On Bahamut use Meltdown and Limit Breakers.

Jumbo Cactaur          Element: None "1000 Needles" [Single]
Name From: Apperance [Well... It looks like a BIG cactus...]
Starting Level:20        Hp:1766    Damage:2000
Level 100        Hp:8150    Damage:10,000
Best skills: Kamikaze, Initiative, Move Hp Up,Bonuses[Hp etc.],Expend2-1
How to get: Go to Cactaur Island East of the main landform East of Centra Ruins, and run into the picture of a cactus to fight him. Use Leviathan and Meteor as well as Meltdown and Limit Breakers.

Tonberry King          Element: None "Chef's Knife" [Single]
Name From:Unknown
Starting Level: 30    Hp:2596    Damage:1492
Level 100        Hp:8350    Damage:3855    
Best skills:LvUp,LvDown,Move Hp-Up,Haggle,Sell High,Fimmiliar,CallShop
How to get: Go to the Centra Ruins and beat 20 Tonberrys without leaving. Immedeately after defeating the last one, you'll he'll appear. He has a lot of Hp, but the Meltdown/ fast Ammo trick does a great job on beating him.

Eden              Element: None "Eternal Breath" [All]
Name From:Unknown
Starting Level: 30    Hp:4786    Damage:5425
Level 100        Hp:9999    Damage:11,500
Best skills: Mad Rush, Darkside, Devour, Expend 3-1, GF Abl Med RF
How to get: After you beat Bahamut in the Deepsea Research Lab go into the Ragnarok and land somewher, then return and you'll find you can go deeper in. There are six floors in the new area.  Here is what you should do.
Floor 1 Use 4 units to open the door to floor 2.
Floor 2 Use 2 units to open the door to floor 3.
Floor 3 Use the monitor on the left side of the room and under the stairs then,    Use 4 units to open the steam room, then recharge 7 units there. Use the second station in the main room to use one unit and open the door to the fourth floor.
Floor 4 Use 1 unit to open the door to floor 5.
Floor 5 Use 1 unit to open the door to floor 6.
Floor 6 Use 4 units to open the floor to the excavation site. Be sure to save.
To beat Ultima weapon use Meltdown and Limits. Draw Eden from it.