Location: Magical Lamp

Diablos is found inside a magical lamp.  To find it, in disk 1, after Headmaster Cid lets you go for your first SeeD mission (the part when Zell gets in trouble), talk to Cid.  He will give you the magic lamp.  It is in the item inventory.  Save before using the lamp.  It is better to fight him once you receive the lamp, so you can use him in battle.

Fighting Diablos

Diablos is pretty powerful at the time you fight him.  He only know gravity based attacks, and he uses them often.  First, cast Protect on each party member.  Cast haste if you have any.  Summon Ifrit and Shiva.  They are the best against him.  Cast Meltdown on him if you have any, and keep attacking him.  When he casts Demi on you, quickly use Cure or Curas before attacking again.  Watch for his Gravija attack.  If you think you're good enough, keep your HP critical so you can use the limits. You will eventually beat him if you keep your HP high. 

Diablos's attacks
Slash
Demi
Gravija

Location: Cactuar Island

Jumbo Cactuar is a tough enemy because he has high HP.  About 115,000 to be exact.  He is weak against water, so junction water to Elem-Atk.  And definitely junction Leviathan.  It will be good if Squall has the Lion Heart as well.  To get to him, simply walk into the green thing popping up and down on the island.

Fighting Jumbo Cactuar

First of all, cast Protect on all the party members.  Then draw Meltdown and from JC and cast it on him.  If you have Aura, cast it on Squall and Zell, particularly Zell if he has Dolphin Blow.  When JC uses his 10,000 Needles move, quickly revive the person or else he will use it again quickly on the remaining party members.  If Leviathan gets KO'd, Quickly Summon Cerberus and cast heaps of Water spells.  Note that when Jumbo Cactuar gets threatened too much, he will run away, and all your effects will be for naught.  So kill him as quickly as possible.  After defeating JC, you will receive the Cactuar GF.

Jumbo Cactuar's attacks
Stomp
Meltdown
Ker Plunk
10,000 Needles

Location: Deep Sea Research Center

Bahamut , the 'King of GF', is quite a tough enemy.  It is better fighting him when your characters are low level, so his attacks aren't as lethal.  Make sure your party members have high HP (Above 5000 will be good enough).  Bahamut is found at the Deep Sea Research Center (See WORLD MAP).  In the room with the light, do not walk when there the light is flashing.  Reach the light and you will be asked a question.  Pick the 1st and only option.  You will fight a Ruby Dragon.  After defeating the Ruby Dragon, you will be asked another question. Pick the second option, Never.  You will fight another Ruby Dragon.  Defeat it and another question appears.  Pick the hidden 3rd option.  You will then fight Bahamut.

Fighting Bahamut

First, cast Protect or possibly Shell on all party members.  Cast Meltdown and Blind on him.  Summon GFs such as Diablos and Cactuar.  Do not summon Quezacotl or Pandamona.  Cast Auras if you have any on Squall, or Zell and Irvine; their limits work well.  You can draw Flare from Bahamut and cast it on himself, and you can also draw Curagas and Full-Lifes to help you.  There's one move you should be cautious about, and that is Mega Flare.  It causes about 4000-6000 worth of damage.  Just keep curing your characters and use GFs and Limits and you'll beat him.  Once you beat him, he will be a summonable GF.

Bahamut's Attacks
Claw Swipe
Thundaga
Aero
Tornado
Demi
Flare
Mega Flare