Some more notes:
The Underground Waterway monsters mainly consists of new creations (well, at least with the palette swapping). This is actually great since lots of existing monsters and formations have been reused a bit... you might as well actually make it distinct at this point.
One of the monsters in that revised dungeon does apply poison... I figure it is the snake monsters.
The Fire Sword (and maybe of the elemental weaponry) is not that useful... so you will have to occasionally pick and choose if you plan on using elemental weapons (it makes you wish Yang was around).
The Chaos Lady (the dungeon specific monster) is a pushover. If you are efficient in killing, Doom is just not threatening...
Most of the monsters in Kain's Challenge Dungeon are generally a mixture of the Tower of Babil (Edge route) with some Summoners on a special floor... and then all the Sylph's Cave and Land of Summoned Monsters combos with creative rehashes. Unlike the original game, your equipment select limits your full defensive potential.
Like the original game, the Diamond Armlet is overrated and should always be a last resort to acquire lightning resistance for the spellcasters... It was key for Edge in the original... The Gold Hairband is the key option.
The Gold Hairband and the Luminous Robe was always a really powerful combo in the game. The both have lightning resistance, but the most important aspect was the racial resistance... Dragons for the Gold Hairband and Undead for the Luminous Robe. Of course, the Gold Hairband was more favorable to Rydia... but nonetheless, it provides what you need for the most part. Of course, the trifecta is the Rune Armlet for Mage protection. That usually covered all the racial resistances you needed in the end game (outside of the sole Giant and Mech, except the EvilMask never attacks physically).
Rosa looks too much like the White Wizard in FF1A... which is lame.
Continuing with tradition, Ceodore can equip some of the same wizard based equipment that Cecil could. The Luminous Robe may actually be better on Ceodore than Rosa... despite the fact Rosa would benefit more.. .but she gets the Gold Hairband, which covers what you need for the most part. Note that there aren't any undead in this dungeon... so that's not why you give it to him... the Ice Shield+lightning based armor combo is great... you get fire and lightning resistance.. all of which you really need in the dungeon. I've never been fond of the Diamond Gloves or the helmet... they suck compared to the armor and the shield.
The Thunder Dragon in this dungeon looks a lot more like the original FF4 version. Unfortunately, if you don't have ANY lightning protection, RUN THE HELL AWAY. Since its Thunderbolt attack is maxHP/2 (with randomness), a surprise attack will allow him to dish almost 4000HP raw damage, killing any character instantly. It's better to fight it when you have given lightning resistance to all characters... then again, the weaker version in Ceodore's version of the Mist Cave is at least twice as easy.
Blessing is not affected by the moon... which is nice (I forget if Pray is).
Cid's Risk Strike doesn't seem to work vs bosses... why bother with the command? It does seem to deal 2 times the damage when it works... but I don't like unreliability in commands if it doesn't work more often than not.
The Sledgehammer adds +5 STR, like Gaia's Hammer. I don't think it's that much of an improvement (like +10 attack power more than the Ogre Killer) when you lose the shield. Sure you will lose the shield later on when the stronger weapons become 2 handed only, but you need the Fire protection vs the Cursed Dragon and Lighting protection primarily against the Thunder Dragon. I guess you can figure out alternate ways of doing it through the diamond armor set, but doesn't allow for Cid to get to his full potential.
With regards to Cid, it's kinda nice to be able to take advantage of a shield... as much as he has evasion like a rock, it's vital as long as you are able to make him really strong, because he's unbearably slow.
Finally, a reason to use the Cross item. The boss on its 3rd consecutive counter attack uses a multitargeted Cross. This is very punishing since you have nothing to block it outside of Mystic Veils... which aren't even applicable to this dungeon or the characters at the moment. I mean there are two major options to killing the Curse Dragon... both options are specific to the "undead" version of the monster...
1) Just Jump with Kain. Since the counter is instant death (seemingly only to Kain), all you need to do is double down on a revive (the spell or item) and then some short healing (basic Rosa's Cura or Ceodore's Curaga will be enough). This may probably be the best option if you don't like what I'll say about the second option.
2) Let Kain do all the work... under Berserk. This allows Haste to be in use, since it goes away when Kain dies. This is preferable in all circumstances that don't affect the attack power negatively (just one of the moons will probably screw this up).
The Curse Dragon when physically attacked does the following (in the order of counter attacks):
Doom - seems to love Kain due to RNG/emulation
Multitargeted Firaga - hurts Rosa the most because she has no elemental resistance, whereas all the men have some part of the Ice Armor set available
Multitargeted Curse - hurts Kain the most in this instance
Dual-hit - seems to target Rosa, then Kain... I'm not sure if this is its natural attack or an actual counter
Restart with Doom counter...
It's insanely easy when Kain does most of the work (if not all of it). Cid is best for using items and Rosa for healing... Ceodore could use Esuna, but that will remove Berserk, so you could set up Rosa to reapply it after Esuna. A Cross will allow you to avoid recasting Berserk.
It is really counterproductive for Cid and Ceodore to attack. Kain's Dragoon Lance is Holy elemental.. which is the weakness of the monster. The strange part is that the "undead" version of the monster isn't actually listed as undead (I'll need to actually see if that is the case). This is Kain's Challenge Dungeon after all...

It's fun when you silence those Mini Satana or Elder Treants and then proceed to put confuse status on them... you'll just end up causing them to attack you. Since the response to confuse status is casting magic, and silence causes all magic to be replaced with a regular attack... you'll see how this result came to be.

I think I was wrong about Saint Dive... since I was testing that on Flan. It seems to do Jump damage with a little bit of variation, and applies Holy elemental to the attack. It's not as much magic (it doesn't seem to be resisted by the Mad Ogre), but Flan do have high defense, which might explain the damage I got (though now, Rosa+Cid are at different levels now, so I will retest).
The Curse Dragon counters are based on the fact that Doom (the countdown) is applied to a character. It will keep attempting to apply Doom until a character is affected, and then it runs through its special attack cycle.
After the Dual-hit from the Curse Dragon, the last known attack is Dark Breath (IIRC, it's fire elemental and very likely based on the monster's HP). There may be more, but Doom's Coundown takes forever.
I had forgotten about the fact that Doom is reflectable. Yes, the spell that the infamous Fataleye/Ahriman uses is reflectable. I don't remember testing it in the PSP version (well, the aspect that it can be applied to a monster with the boss bit), but in TAY, it won't work. At least preventing it from working is the best thing you can do... So, it is beneficial if either Rosa or Ceodore (preferably both) is able to cast Reflect on Kain (and probably the others, since I figure the RNG is probably emulation related) to keep the Curse Dragon from doing nastier things. Its attempts to apply the status is crucial for you to not take any damage... but it is more crucial for the monster to be execute the other parts of the script.
The Obelisk Lance is probably the weapon of choice of Ceodore. The Dragoon Lance is still vital to Kain anyways. Although the Demon Slayer is a decent weapon, there shouldn't be any "Demons" outside of the Lamias that you will be fighting and the weaker creatures outside of Baron. You need weapons to annihilate the Thunder Dragon and other flying monsters and the Obelisk Lance is that weapon. Plus, it's the strongest of the bunch, with +5 STR to boot. Too bad the STR bonus doesn't really lead to an increased attack multiplier for either Ceodore or Kain... oh well.
The Elfin Bow is still effective vs Mages, despite that not being listed (like Rune Armlet's resistance to Mages). Strangely, Shell can be cast on all characters... unlike the Protect Staff's solo targeting. The Elfin Bow still retains +5 INT.

Some worthy notes:
Cross Slash Prime appears to be closer to a combined attack between Ceodore and Kain with doubled damage.
Saint Dive is like having a holy elemental Jump targeted to all. When used against Flan, it does nice damage, but it feels like reduced damage (like 1/4 to 1/2 less damage), since most of the work has to do with Jump.
X Chaser seems to ignore defense when the damage part is applied, but the damage is strictly what Rosa would do to the monster. So, it's reliant on the instant death attack to high defense monsters.
Rocket Launcher deals damage close to 50% more than what Ceodore normally does, I think. However, it is obviously more effective if its targeting monsters with the weakness of Fire. It's not really that good otherwise. I will have to look at the damage soon.
I haven't use enough of Aiming Thrust to get an idea of the damage dealt when Instant Death is not applied.
I've collected all the items in Kain's dungeon, but I haven't gotten the Grey Tail yet.