Disclaimer: The below posting is not something I wrote, but merely a post from another board I frequent that has a lot of useful info. Posting it here for the fellow Rerollers. Credit: Pokefan from Gamefaqs
Two more major members of FFIV's cast debut in this event. Edge is both Ninja and Thief, and capable of using Fists, Throwing, and Katanas. Rosa is your basic White Mage, though she does have the uncommon Support 4 in addition. This event also introduces the Memory Crystal II for the Dark Knight Cecil. Though a very limited and inflexible character, his Record Materia and future prospects make him arguably worth leveling.
To go along with Edge's arrival, more Ninja abilities are introduced. The 3* Water Veil is a Water-element counterpart to the Swift Bolt, with the same reduced casting time and defense-ignoring properties, while the 4* Shadowsteel attacks the enemy and may inflict Sap, making it the only ability capable of inflicting Sap. Lastly, the 3* Dragoon skill Ice Jump is introduced, adding another element to the Dragoon arsenal.
Equipment List:
2x Mage Masher
2x Ice Rod
2x Sage's Surplice
Stage 1 - Mist Dragon
Special Score: Don't get KO'ed
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At a mere 25k HP, Mist Dragon should go down in a few good hits (a strong Roaming Warrior could finish it outright). After several actions it will turn into a Mist form, so if that happens, simply wait for it to reform. It's weak to Dark and absorbs Holy. Both Rydia's and Cecil's Memory Crystals are easily obtainable here.
Stage 2 - Magus Sisters
Special Score: Don't get KO'ed
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Sandy uses support/status magic, Cindy uses basic attacks and heals, and Mindy casts offensive tactic. As the originators of the infamous Delta Attack, Sandy will cast Reflect on Cindy, and Mindy will bounce spells off of her. Sandy and Mindy can be Silenced to shut down their spells if needed, leaving them quite useless. Though Cindy is the most durable of the three, you may want to focus on her first, as she may revive her fallen sisters. You get Kain's Memory Crystal and an Ice Jump from this stage.
Stage 3 - Barbariccia
Special Score: Rosa is alive in the party
Dispel Barbariccia's Tornado form with 'Jump'
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Strangely, Rosa is a required character to master Babariccia in her Elite incarnation. She has about 65k HP. If you want the special score condition you'll have to bring a Dragoon and wait for her to randomly enter Tornado form; outside of it, she's vulnerable to Paralysis and can be stopped with Intimidate while you wail on her. Earth and Wind attacks don't work very well on her, but other elements are fair game Rosa's Memory Crystal is in this stage.
Stage 5 - Calcabrina + Golbez
Special Score: Don't get KO'd (x2)
Defeat Calcabrina before they combine
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The Calca and Brina have about 14k and 11k HP respectively; a few good AoE attacks should wipe them out long before they get the chance to combine.
Golbez starts the battle by summoning his Shadow Dragon - they have about 74k and 55k HP respectively. Golbez uses Barrier Change to shift his weaknesses between Fire, Ice, and Lightning, but Holy is a permanent weakness of both him and the Shadow Dragon, so Dia spells work quite well here. As Golbez's arsenal consists largely of single-target magic, using a Carbuncle and mitigating the physical attacks of the Shadow Dragon will keep down the damage. Anyways, defeat the Shadow Dragon first; its Black Fang causes instant death. Another move to watch out for is Golbez's Binding Cold, which paralyzes your party. Hope those two moves don't get used. Golbez's and Edge's Memory Crystals are obtained here.
Stage 6 - Dr. Lugae/Barnabas + Lugaeborg
Special Score: Defeat Barnabas before it explodes
Exploit Barnabas's Lightning weakness
Exploit Lugaeborg's Lightning weakness
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Another 2-boss stage...for the first one, Lugae has about 27k while Barnabas has 37k. You can defeat them in any order, but if Barnabas is defeated first, Lugae will take direct control of it, so defeating Lugae first may be more efficient. Still, defeating Lugae will make Barnabas unstable and cause him to explode, so be sure to defeat Barnabas soon afterwards. Lugae does not attack while Barnabas uses purely single-target physical attacks, and he's also weak to Slow.
Lugaeborg has about 82k HP, and uses a mixture of physical and magical attacks, so be sure to pack mitigation for both. He still has the Lightning weakness and Slow vulnerability. His only special gimmick is that he might counter attacks with Sleeping Gas. The prize includes a free copy of Water Veil.
Stage 7 - King and Queen of Eblan + Rubicante
Special Score: Edge is alive in the party (x2)
Exploit Rubicante's Ice weakness
Exploit Rubicante's Water weakness
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This seems to be a theme by now. The King and Queen of Eblan simply use all-target Fire spells; use Magic Breaks and Shellga to reduce the damage taken. They're vulnerable to Slow as well, which can be helpful (it's recommended to get it on the King first, as he's stronger). Both have about 72k HP and you only need to defeat one to end the battle.
Rubicante has about 115k HP. He absorbs Fire and is weak to Ice and Water normally. Still, whenever he uses Inferno, he'll go behind his cloak (when he does so and how long he stays is random) and in that state the elements he's normally weak to becomes absorbed. Protect yourself against his Fire magic and pelt him with Ice and Water attacks while he's vulnerable. Since he may counter physical hits with an all-target Fira, a magic-heavy approach is more recommended. Slow, and if you have it, Sap both work on Rubicante.
Stage EX - Sealed Treasure Guardians
Special Score: Don't get KO'd (x3)
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Now you're in for it...
White Dragon: 74k
Dark Bahamut: 83k
Ogopogo: 87k
Three of the most difficult bosses in FFIV, as a set. Perhaps the scariest boss rush that there is. Since all 3 opponents have great elemental resistances, and Ogopogo counters magic, it's best to go with a physical-heavy team. If you really want to use a mage, only Non-Elemental and Poison spells are acceptable, and you may want to try fitting in a Reflect as well. Either way, pack mitigation against both physical and magical attacks (with an emphasis on magic), and be sure to bring a Dispel for Dark Bahamut. Since Dark Bahamut and Ogopogo start off ambushing the party with deadly magic attacks, AoE healing and/or Heavy Regen would be a big help in patching up your party. The only status vulnerabilities they have is to Sap and (Ogopogo only) Slow. For defeating them all you obtain Shadowsteel.
Stage EX+ - Odin
Special Score: Don't get KO'd
Cecil (Dark Knight) is alive in the party
Exploit Odin's Lightning weakness while he has his blade raised
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Though skipped over by the main Realm dungeons, we finally get to fight Odin! He's got about 187k HP and is rather simple for an EX boss. He uses nothing but physical attacks, so you can focus all your mitigation on that. Retaliate users are entirely untouchable, while back row characters take reduced damage. Odin may randomly raise his sword; this is a signal that he is about to use Zantetsuken, and he also gains a Lightning weakness while in this state. Exploiting that vulnerability is a nice option, but so is guarding. As far as status effects go, he is vulnerable to Slow. Incidentally Odin breaks the rule that Poison hits neutrally on all FFIV bosses by actually resisting Poison attacks. Defeating this Eidolon nets you Cecil's Memory Crystal II.
Stage EX++ - Geryon
Special Score: Don't get KO'd
Inflict Slow on Geryon
Inflict Sap on Geryon
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Geryon's got about 218k HP. Though this bonus boss may not be quite as tough as you might expect from a bonus boss, good god is he/she annoying - or should I say, malicious, on so many damn levels. The biggest culprits are his/her Scarmiglione moves, Gas and Cursed Elegy; the former randomly inflict Poison/Blind/Silence/Sleep on the whole party while the latter is used as a counter to physical attacks and inflicts Slow on the party. He/She also gets Maelstrom and Ray from Barbariccia to reduce an ally's HP to 1 or Petrify an ally, as some more annoying little features.
Though one would wish to use a magic-heavy team and keep physical attacks to a minimum to avoid at least Cursed Elegy, the only Sap-inflicting ability is a physical move that you'll likely be forced to use multiple times. Magic mitigation such as Magic Breakdown is also important since, when Geryon actually attacks, his/her main threats come from AoE magic. So just hope he/she doesn't use it...or any of the other status moves that'll induce an S/L. Using status-resistant equipment on key members can help a little. Geryon absorbs Earth/Ice/Wind/Fire.