This is Via Purifico, Bevelle's supposedly inescapable dungeon which the party has found themselves in. They have been separated into two groups. There's Yuna, Kimahri, Lulu and Auron in the dry section and Tidus, Wakka and Rikku in the underwater section.
You'll first gain control of Yuna, alone, in Via Purifico. There are enemies down here, so until you get more party members, you will have to summon in every battle. The monster encounter rate down here is pretty low, but there are new enemies (although a lot are improved versions of previously encountered fiends, and none of them can be captured given that you can never return here). Ixion does the job quite nicely, since a lot of enemies are Water-aligned. Shiva can dodge most attacks and does fair damage, and against crowds of enemies Bahamut does an even nicer job with Impulse. It is wise to save any Aeon overdrive if you get it, though.
Before you carry on out the top of Via Purifico, search around for some chests to pick up stuff you can't come back and get. If you look on your mini-map, other arrows indicate your other party members, so pick them up as soon as possible. In the same room as Kimahri there is a chest with a Mega-Potion, and he's located on the right-hand side of the dungeon. Auron's at the top of the area by the Save Sphere. Lulu is on the left-hand side of the dungeon right next to a chest with a White Magic Sphere (this allows you to activate any White Magic tile on the Sphere Grid previously activated by an ally). In the bottom left room, there is a Destruction Sphere glyph you can touch (this is very significant) and a chest with an Elixir.
If you head along the middle of the dungeon, in a side room with a chest containing a Black Magic Sphere is another Destruction Sphere glyph you can stand on, which will cause a warp pad to move. Use the nearest warp pad to jump over to the moved pad, which activates it. Use the moved pad to get past the gate into a side room. Here you can pick up a Lucid Ring, Skill Sphere, and to your south is a chest containing 10,000 Gil. Head up and out the top, through the path with the red lights. You'll meet with Isaaru at the end, who's been ordered by the temple to stop you. He's going to use his Aeons to do it, so you're going to have to beat him in an Aeon duel to the death.
Isaaru's Ifrit, Grothia
Unfortunately you start in the rough right from the beginning, since it begins with a full Overdrive. Summon Bahamut or Ixion and have them use Shield to take the brunt of Hellfire (this will either kill them or drop them into critical if you don't). However, Grothia is pretty weak strength-wise and really slow, so even Bahamut should be able to get a double turn in. Use Blizzaga (as Ifrit is Fire-elemental) and physical attacks, then top it off with Mega Flare once you get an Overdrive. It shouldn't last long, since Grothia doesn't have that much health (you might not even need to use Mega Flare).
Isaaru's Valefor, Pterya
Bahamut works well again (especially if you compound it with three-tier magic and Mega Flare) or if things didn't go to well, Ixion/Shiva. Valefor is a little quicker than Grothia and a little more evasive, but is still slow enough to grant Bahamut the occasional extra turn, with Shiva regularly getting them. Don't worry about Mega Flare doing less damage than Thor's Hammer or Diamond Dust, because Mega Flare and the rest of Bahamut's attacks can exceed the damage limit of 9,999 without the unsealing of any celestial weapons and soon Mega Flare will be doing over 10,000 damage. But for now it'll do about 7,000. If it abuses Sonic Wings and unleashes an overdrive on you, then Bahamut might find itself in a bit of trouble, but don't worry, it's not difficult and you can always summon another aeon if it dies.
Isaaru's Bahamut, Spathi
Spathi has a truckload of health and is pretty fast for a Bahamut (able to keep up with Shiva, who you should summon for this battle), but its only attacks are a countdown followed by Mega Flare. As you can guess, this is an instant kill for an unshielded aeon. Shiva should use physical attacks (don't use Heavenly Strike since Spathi is immune to delay) until you get to overdrive when she should use Diamond Dust for 9,999 damage. If you're lucky with critical hits and turn order, you may be able to kill Spathi before he unleashes one Mega Flare. Otherwise, heal up with a Blizzara on herself and then keep attacking. It's unlikely that Spathi will live to use another Mega Flare, but if shielded the damage drops to below 600 which is more than survivable for Shiva.
Once that's over, you'll carry on out of Via Purifico. Yuna will get AP and money, and you'll hear the boss battle theme once again.
In this section, you have three characters; Tidus, Wakka and Rikku. You must swim along the chamber and you will have to face random battles (unless you are lucky enough to have a piece of equipment with No Encounters) and fight another Boss. Swim along to the large doors into an open section and save along the way. If the monsters down here are giving you a bit of trouble, Tidus' Slowga is a godsend and will give you lots and lots of turns. Save again and enter the open area, and you'll meet an old friend.
Boss Battle: Evrae Altana
If Evrae Altana was anywhere remotely close in strength as he was when you fought him last, this battle would be nightmarishly hard with just Tidus, Wakka, and Rikku. Although there's a "proper" way you can fight this, the easiest and cheapest way to beat this guy is to use two Phoenix Downs on him. Each one will hit for precisely 8,192 damage, which is exactly half of his 16,384 HP. You can also choose to fight him in the traditional manner. Watch out for Stone Gaze, since this will instantly petrify and shatter a character if it connects. It will hit you most of the time without intervention by armour with Stone Ward or Stoneproof. Since you've only got three to choose from and nobody else, this is even worse than it was on the Airship.
Each one of Evrae Altana's physical attacks can do about 900-1,000 damage to one person. Photon Spray got a minor power upgrade from the airship one, now doing about 150-200 damage per hit, and hitting more often. It lost Poison Breath however, which is good. Evrae still has an annoying habit of counter-attacking, but it's not nearly as bad as it was on the Airship (it can't use Haste either, which is a bonus, and its resistances to Slow and Darkness have been dropped a little). Opening gate locks will cause the battle to begin anew further along, although you miss out on stuff by doing so. Use this if you're in trouble, since the restarting of the battle (Evrae stays at the same health as he was when you fled) will bring back any shattered characters and any KO'd characters with 1 HP.
This battle is very easy if you use Phoenix Downs or X-Potions (if you saved them, each deals 9,999 damage or more), as mentioned above. Just make sure you let everyone take a turn and you get an Overkill and two Black Magic Spheres. The chests along the first section of the underwater tunnel contain a Rematch and an Avenger (weapons for Wakka and Tidus respectively). Once you get to the end, you'll be reunited with the rest of your party. Unfortunately, Seymour shows up, and you'll see him get a big upgrade.
Fighting along the Highbridge
Kimahri will take it upon himself to hold back Seymour, but obviously he's not going to do much. You've got to actually get all the way back to him, and you'll be contending with the same combinations of enemies as you did up on the wedding platform, so check back on the Bevelle page for the tactics to beat them. Any Overdrives you get, you should save for Seymour since he's quite difficult. Getting Aeon overdrives will help, but is not absolutely essential. Even though you're a traitor, O'aka will still sell you stuff, although there's no equipment available from him, just items. Stock up on Soft if you don't have any or only a few, since you'll be dealing with petrification in the next battle. Once you reach the end, you'll meet up with Kimahri and fight Seymour.
Boss Battle: Seymour Natus and Mortibody
Seymour banishes Aeons a turn after they appear (instant death, unavoidable) so that's the only time for an overdrive. Even then it takes quite a bit to defeat Seymour, since not all of their overdrives will do 9,999 and Seymour Natus has 36,000 HP. The Mortibody is a separate boss that can't be defeated — it has 4,000 HP initially and every time you deplete that amount, it'll use Mortibsorption and take a decreasing amount from Seymour. It starts at 4,000, then 3,000, then 2,000, then 1,000, and will remain at 1,000 until Seymour dies. This is a good way of dealing damage to Seymour, by using multi-target attacks and letting the Mortibody deal some more damage for you.
This also means that Seymour has two ways he can hurt you. The Mortibody attacks always compliment what Seymour uses, and that can be any number of things. Seymour has kept his black magic spells and will cast multi-aura spells on two people for about 1,000-1,500 damage. The Mortibody will use the lowest black magic spell of the same element on everyone, but it does less damage (about 300). This will rid your party of the Nul spells if you cast any, leaving you wide open for Seymour. If Seymour starts using Break or the Mortibody starts using Shattering Claw, then that demands a new strategy. Get Rikku out and have her repeatedly use Al Bhed Potions (or Soft) to get rid of the petrification, because Break inflicts it with almost a perfect success rate (without any resistance from armor, that is) and Shattering Claw does exactly what it says — shatters people if they're petrified, otherwise doing about 300-700 damage.
Flare is Seymour's other trick, which is complimented by Dispel or Desperado from the Mortibody. Dispel removes all positive status effects from you party, and Desperado does that as well but inflicts about 800 damage to everyone alongside. Flare does about 3,000 damage to one person, so with the exception of maybe Auron, this is pretty tough to survive since Shell will most likely be taken off by the Mortibody before Seymour uses Flare. Mortibody will start curing Seymour. When he does this, cast reflect on Seymour and he will keep curing your party. Unloading Overdrives on Seymour is the best way to go about fighting this battle. Make sure you end it quickly because as your party becomes weaker it becomes harder to keep up with Seymour's attacks and the Mortibody's complimentary moves. Outside of Seymour's usual chain of attacks, he may cast Protect or Shell on himself. Talk can raise some stats, but it's not really worth it.
Alternately, Reflect makes this battle very easy. Because Seymour and the Mortibody rely on black magic spells to inflict high damage, by keeping Yuna with your two highest physical damage dealers and having her cast reflect on everyone (including Seymour, since the Mortibody will try to cure him after draining him), Seymour takes damage on your turns and his. You can still cast spell attacks if you choose to, by targeting one of your party members and letting the enemy take the damage.
Once you're finished with Seymour, he'll die again and you'll be off to Macalania Woods once more.