It's already been a couple days since 4.2 went live, but I thought I'd compile a sort of mini-guide to the normal version of the Sigmascape raids. There's a lot of unique mechanics to talk about, and after going through each fight and reviewing a few things I think I can touch on most of the important things of note.

V1N - Phantom Train
The first fight has a few things to watch for. Firstly, a couple box-shaped AOEs will launch and leave a purple spot with a ghost where they went off. Avoid walking into these if you don't want to die.
The boss will sometimes ram into the platform, which will be telegraphed by the purple wave impact indicator (meteor mechanic). Players will get knocked back after this goes off.
Players will periodically be tethered to ghosts, and players will also be followed by a searchlight circle on the ground (think the Scorpion boss at Ala Mhigo). The tethered players want to lead the ghosts to where these lights stop, as they create a pillar of light that'll kill the ghosts (but try not to get caught in the light yourself.
You'll also see a stack marker that looks like a row of arrows instead of the usual cross-shaped indicator. Stack up in a straight line with the targeted player to split the damage.
Ghosts will also line up at the sides and slowly move across the platform. Just dodge them.
Partway through the fight a blue floor indicator will appear as the boss moves to the side of your platform. Step on it to be launched on top of the Phantom Train and move to it's front. Here you'll want to kill the chimney stack add as quickly as possible to do considerable damage to the boss.
After that you'll be sent back to the main platform, and iirc this is when more ghosts appear. This time you'll need to let one of the ghosts catch you, and you'll be teleported inside the train to fight an add. If you take too long to catch onto this (like I did), anyone who doesn't get caught by a ghost in time will instantly die. Kill the add and return to the platform.
Two players will also get targeted for another indicator with orange impact waves (like the last boss of Doma Castle). Bring these to the corners away from the boss and quickly run back to the front to reduce impact damage.

V2N - Chadarnook
This boss is actually fairly straightforward, despite appearances. You'll get a duty action (Chocobo Brush) to use on the four canvases on the floor throughout the fight. The boss will move to the center of the room and begin tethering to one of the four paintings in each corner. We'll say the point where the boss starts at is N, and where the raid starts at is S. Roughly, each painting will work as follows, in the order I remember them:
SE painting - This will let the boss do a heavy fire attack when cast. Everyone will need to stand on the canvas in front and use the duty action to get a water buff that will protect you from the attack.
NW painting - This will project a mist attack. Have a person quickly use the duty action on it's respective canvas to summon a large boulder. You should probably know what this means from previous bosses: Stand so that the boulder is between you and the painting to shield you from damage.
SW painting - This will summon several orb adds all around the room that can't be killed conventionally. Each orb will cast a fatal AOE around it, killing anyone caught in a blast. The first player to use the duty action on the canvas will turn into Typhon, giving them an ability to get rid of the orbs to create safe spots. Keeping the area near the boss clear should more than suffice.
NE painting - Will cast a roomwide earthquake attack. Everyone will need to use the duty action to summon a plane mount. Stay on the mount until the attack goes off, then dismount afterwards.

Basically, west side = one person uses duty action, east side = everyone uses it. Once all four have been used once, the boss will begin to use combinations of two paintings at once. Simply use each respective canvas to counter it before the attacks go out. Other than that, watch for the occasional AOE, as well as players being marked for a splash AOE that will follow the targeted players and repeat the attack a few times. You might want to pop Sprint to keep ahead of the attacks, and watch for other players so they don't get caught too.

V3N - Guardian
This is where the suffering begins... First of all, beware the edges of the room, which will damage and paralyze you if you run into them. The boss will also charge a laser beam which will be a large frontal cleave to everything in front of it. When you see the laser charging, GET OUT OF THE WAY IMMEDIATELY! You'll see two monitors at the north end of the room: The big one shows which battle program the boss is currently using, and the smaller one shows what it'll do next. Each of these programs does attacks based on several FFVI bosses. Before shifting to the next program, it will also summon an add that corresponds to the program it is currently running. Here's a rundown of what I remember:
Air Force Program - Airplane sprite on monitor. As soon as you see this, get ready to move away from the boss to dodge the AOE that appears around it. It will summon several slow-moving missiles around the room. I believe they will change direction once while making their way through the room. These need to be dodged, naturally. After these mechanics, the boss will summon the Air Force add. Burn it down quickly.
Dadaluma Program - Martial artist sprite. When you see this come up, get ready to move close to boss. The boss will do a knockback move, so you need to be positioned in a way that doesn't get you knocked to the edges. Several green-ish yellow circles will appear on the floor with aura orbs descending on them. A player must stand in each of these (not sure what happens if any are missed, but let's not try and find out shall we?). Boss will summon the Dadaluma add here, which needs to die fast.
Ultros Program - Purple Octopus sprite, if you're not familiar with this scamp already. The boss will throw several AOEs here: One set will drop ink where marked, another will summon several giant tentacles. After the tentacles appear, they will telegraph several straight-line AOEs in the direction of certain players. Dodge accordingly. Boss will then summon the Ultros Add. Standard protocol here.

The final program is a bit different and also a blast from the past (also somehow the mechanic that confused people the most in the fight?), the Bibliotaph Program - Remember this guy from the Great Gubal Library? When the boss uses this, several purple circles will appear on the floor. Three players will need to stand on each platform at the same time to disengage it. I recommend two groups of two DPS and one healer split up north and south, then move either clockwise or counter-clockwise (party can decide beforehand) to quickly remove these. You may remember failure to remove a circle will summon an add. Trust me, you want to keep adds to a minimum here. The Bibliotaph add will be summoned at the end, and the more adds from the previous mechanic you allow to be summoned the quicker the raid is likely to get overwhelmed and eventually wipe.

V4N - Kefka
This is fight is incredibly unique, as well as aesthetically pleasing. First of all, watch the edges of the platform, as you can get knocked off and fall to your death. The main thing to note throughout the fight is that AOE telegraphs are not always as they seem. Kefka likes to trick you into thinking your safe, and then blast any part of the platform that isn't marked by the telegraph. So how can you tell where to stand when he's about to launch one of these attacks? When you see a solid purple telegraph, and the orbs floating around Kefka are also a solid color, stand outside the telegraphs like normal to dodge. If you see question marks on the telegraphs as well as in the floating orbs, stand in the telegraphs instead. These will show up either as a circular/donut AOE around the boss (Blizzard) or multiple straight-line AOEs (lightning). I know he has a tankbuster (Hyperdrive, I believe it was called), but I don't know if it has any debuffs as I am not a tank myself, but I don't believe there were. I'd definitely like a tank's input on that though.

Once you whittle away a bit of his HP, a giant statuesque tower will appear near the platform representing the different tiers of FFVI's final battle. You will need to be watching the statues for each tier to respond to their mechanics. The first tier will shoot an orb to one side of the platform, and will act much like Shinryu's Tidal Wave. Basically move to the edge near this orb so you don't get pushed off by the knockback. The statue will also fire some AOEs, which are dodged like normal here. Kefka will also start using a stack attack occasionally here. Stack up to share damage, but watch out for the his trick AOEs and group up in the appropriate safe spots.

Kefka will also start using the raid-wide Ultima Upsurge periodically to deal some pretty heavy damage to everyone. He'll also do a Timely Teleport, signaled by a large circle appearing on the floor around him and another circle on one edge of the platform. A tower of light will appear for a moment, and he'll appear on the tower opposite of his original location. Immediately after, he will do one of two things: He will either fire a huge beam cleave straight ahead (usually towards the center of the Platform), or he will take a couple seconds to charge Aero Assault to do a knockback. Before the teleport completes, everyone should run to one side of the tower he's moving towards, keeping behind a bit of possible, to avoid the cleave. If it is the knockback, simply run between him and the center of the platform to avoid being pushed off.

The second tier statues will have an orb appear on one side of the statue. Quickly find out which side the orb is on and the run to the opposite half of the platform to avoid being hit (similar to Hashmal's Extreme Edge). Not much else of note here.

The final tier of this fight is the bulk of the fight (occurs when Kefka is around 60% HP iirc). Here, the statue will show one of either two eyes. The purple colored eye means you must look away from the statue before the cast goes through. The yellow question mark eye means you must look at the statue for the cast. All the while, Kefka will continue cycling through all his other mechanics, so you'll have to mind his AOEs at the same time the statue begins casting its mechanics. At this point, you've pretty much seen all the mechanics, and the rest becomes a matter of dodging and burning down Kefka until he finally goes down.

So there you have it. That's all the info I can provide for now. I'm sure I probably missed something, or misunderstood something. Feel free to add in any corrections or other tips if you know of any, and happy raiding!