I've hated the Yellow Plate method to defeat the Criosphinx, and I was determined to beat the Criosphinx using only items that could be obtained from stealing from common enemies, forging from common materials, and purchasing from shops. Here is what I ended up using:
Star level: 32
Lynx
Stone Swallow, Stone Mail, Yellow Brooch, Mythril Helmet, Silver Pendant
Lvl1: Revivex3, Cure
Lvl2: Heal
Lvl3: CurePlus, RecoverAll
Lvl4: HealAll
Lvl5: ||Earthquakex5, Carnivore
Lvl6: ||ThundaStormx10
Lvl7: Carnivore
Fargo
Stone Sword, Stone Mail, Yellow Brooch, Stone Helmet, Silver Pendant
Lvl1: Cure
Lvl2: Heal
Lvl3: CurePlus, RecoverAll
Lvl4: HealAll
Lvl5: ||Earthquakex5, CureAll
Lvl6: ||ThundaStormx10
Lvl7: Carnivore
Marcy
Granite Glove, Stone Mail, Yellow Brooch, Mythril Helmet, Silver Pendant
Lvl1: Cure
Lvl2: Heal
Lvl3: CurePlus, Recoverall
Lvl4: HealAll
Lvl5: ||Earthquakex5, CureAll
Lvl6: ||ThundaStormx10
Lvl7: Carnivore
Note that these characters were also not very "trained up." Fargo and Marcy had only been available since 29 stars. I had been avoiding quite a few battles, so Lynx was definitely not trained to his whole potential (had around 430 HP).
Anyway, the strategy has five simple steps:
(0. Steal the Rainbow Shell)
1. Let two characters die
2. Get them back alive
3. Trap ThundaStorm, Earthquake, and ThundaStorm in that order
4. Heal
5. Repeat steps 3-5 until the Criosphinx is defeated.
The first step is important. Around 8 stamina points into the fight, the Criosphinx will continue to cast Earthquake->ThundaStorm in a cycle until 0-1 characters are left standing. In fact, if you go in with multiple Yellow Plates an infinite loop occurs! To cause the least hurt, go in with the two characters that have no Revives with only 1 HP. The first Earthquake will kill the two, and the barrage will end (you will then see ThundaStorm->Earthquake->ThundaStorm flash in the corner for some glitchy reason, but the spells are never actually cast).
The second step is the hardest. You must now get your team back on their feet with enough HP to survive Earthquake (not to mention the two sets of physical attacks of the Criosphinx). Additionally, you need to set up the ThundaStorm trap. I don't remember the specific number of attacks I used to build up the element levels in the process, but there were a few stamina points to spare before ThundaStorm was cast.
The third and fourth steps are simple repetition. Just like 50% of the enemies in the game, the Criosphinx follows an extremely rigid cycle of moves (the other 50% are reactive, like the Marbule Sage and Dario). The sphinx moves once every 8 stamina points or so. Here is the exact pattern from the moment his initial barrage ends:
A single attack
Two attacks on a single character
ThundaStorm
Earthquake
Earthquake->ThundaStorm
Three attacks on a single character
So once Thundastorm is trapped, set the Earthquake trap. Once Earthquake is trapped, set a ThundaStorm trap. After ThundaStorm is trapped, have a character use HealAll, CureAll, or some other alternative. As soon as it looks like all characters will survive an Earthquake, you should set the next ThundaStorm trap. If the trap is set AND all characters would survive an Earthquake (this happens occasionally throughout the fight), tap into the Carnivores and the character-specific techs. Otherwise, just clean up with the CurePlus, Heals, and Cures.
By the end of the fight I had trapped 7 Earthquakes and 14 ThundaStorms. I never had to tap into that third Revive, and I had several HealAlls left. I never even used the CureAlls.
Now, I did this in a fairly minimal way on purpose. If you have things like Gold Pendant, Momento Pendant, Yellow Plate, Mastermune, Moonglasses, Defender, Defender Plus, Prism equipment, FullRevival, HolyHealing, etc., use them along with this strategy to make the fight much easier. Additionally, I would assume that filling the level 1 spot with TurnGreen and getting rid of the Green healing magic with more white and blue would probably make the fight go even more smoothly. Also, Carnivore is not the right answer in that case. Just like Dario, this fight is really simple and repetitive if you have a plan. Well, I hope this helped somebody.
One more odd thing: Has anybody noticed that the Criosphinx sometimes admits defeat after it makes a move, not after getting hit by you? I've also heard argument over how much HP it actually takes to beat it, some saying that the strategy guides list a lower HP than it actually takes. Is it possible that the Criosphinx has some sort of a timer (possibly stamina based) to decide when it is defeated?
