Yes, I know I skipped Royal Atheneum (a great example of Orphaned Etymology) but let's just go ahead to talk about this far superior raid wing. Really, the Atheneum seems to be where they put their dullest fight (I don't mind Etraeus) while this is a lot cooler, and has the added benefit of being entirely composed of characters we've seen before.
The biggest challenge, though, is going to be finding the bosses. Nighthold is a seriously non-linear raid, and these guys are not in an obvious order. I do think there is a set order, so I'll go with the one we used.
Tichondrius, the leader of the Nathrezim whom we last saw during the Third War getting slaughtered by Illidan (in a way that I really thought was permanent...) is in a building to the right as you start the raid (opposite the one where Star Augur Etraeus was.) There's some nasty trash here.
Tichondrius has there phases with transitions between them. The basic gist is this: he has an aura that gives adds a super-powered Leech effect, so tanks need to pull them away. The tank-swap debuff actually has adds spawn fixated on the tank, so you need to run the adds away to kill them. During the first phase, those are the only adds you get.
The other effect to watch for is that he'll do this void burst ability that hits everyone in line of sight. Conveniently he also summons fel spires that can break line of sight. So just get behind those.
When transitioning between phases, he'll disappear and summon a ton of bat adds that need to be scooped up and AoE'd. Tichondrius will also shoot beam attacks across the room during this phase, which you'll want to dodge.
One phase two, Tichondrius starts to summon in Nightborne adds roughly each time the tank gets debuffed. At least in LFR these guys go down fairly easy, but just try to round them up if you're out with the blood adds.
One phase three, he also summons in a demon with the Nightborne. Same basic deal.
Getting to Krosus means going to the southeast corner that points to the Tomb of Sargeras.
Krosus is a damage race fight. You're on a bridge that has three sections. Krosus will slam on the bridge and I believe every three times he slams, he'll destroy that section.
Tanks have a standard tank debuff, but they'll also need to absorb his slams. You'll see two brown circles where his fists are going to come down. If you take the hit, you'll get a moderate amount of damage and prevent the raid from taking a large amount of damage.
If there aren't any brown circles, that means that the part of the bridge you're on is about to collapse. So get the hell out of there and run back to the next segment.
Krosus will also occasionally fire a Fel Beam, which damages everyone standing on one side of the bridge or the other. He telegraphs this, so be sure to move when you seem him starting to cast it (unless you're on the safe side already.)
He'll also call down fire that hurts anyone it hits, but will hurt the whole raid if it doesn't hit anyone. This is the sort of thing where individual characters should step in and absorb them.
He'll also target random raid members with an Orb of Annihilation (not tanks) which deals a bunch of damage to them and deals damage to the raid based on how far each player is from the target. So if you have this, run to the back (of course, over the fight you have less room to run back.)
Now, the two obvious doors to the Nightspire are still closed. So go back to Tichondrius' room and you'll find a door that leads to a little walkway with some trash. Take the glowing teleporter-orb up to Elisande's room. There's a bit of trash there and then you get to fight the Grand Magistrix.
Elisande does some funky time stuff here. There are three phases - when you get her down to 10%, she'll rewind time and go back to full health. She does this twice. Some effects (though I don't totally recall which ones) will persist through the rewinds.
One phase one, you'll have a simple tank-swap debuff and some adds that spawn. The adds will leave bubbles of accelerated or decelerated time when they die. These become useful when rings of arcane magic move in from the edges of the room. The little balls of arcane will slow down or speed up in the bubbles, and that gives you an opening to avoid them (though in LFR the damage is pretty low.)
One phase two, the tank-swap debuff becomes something where the tank explodes with arcane damage after a few seconds, so you'll want to get away from the raid when the other tank taunts. There will also be these orbs that fall toward the ground that players have to catch so that they don't hurt the whole raid.
One phase three, there is a new tank-debuff that will now persist for the entire fight, but the attack can be interrupted. Try to interrupt this as much as possible to reduce the stacking debuff on the tank (and swap if one tank gets too many stacks.)
Interestingly, once Elisande is killed, her echo will concede that she was wrong - there is a possibility for survival that doesn't involve allying with the Legion. She then promises to do what she can to aid you in your fight with Gul'dan, as you are now her peoples' best hopes. Nice to see a villain who is genuinely just trying to do what she thinks she has to.