I've got a bit of experience in Trial of the Crusader now, so I figured it's time to share some of my experiences thus far. I've actually swapped between both Disc and Shadow specs for this fight, so I may give some healing tips every now and then, but for the most part I'm going to focus on Shadow Spec tactics.
Phase 1 - Gormock the Impaler & The Snobolds
For the first phase of this fight, we've got a huge Magnataur to kill. Most of his mechanics you can ignore if you're DPSing, they're more of a concern for the tanks and healers. If you don't have a Priest healer in your group, you may occasionally want to toss a PW:S on a tank every now and then to ease the tank swaps and help releave a healer for a bit, but mostly you're just DPSing the crap out of Gormock.
What you do want to watch out for though, are the Snobolds. These guys will hop on a random raid member, and start harrassing them. They can deal damage to the raid member, stun them, and interrupt casts (causing long school lock outs).
HOw you deal with these guys depends on who they land on. If they land on a tank or a healer, focus on them and take them down fast. If they land on another DPS, I tend to put up SW:P and VT on the snowbold, cast MB if it's off CD, and a couple Mind Flays before going back to the boss.
If everybody in the raid focuses on Snowbolds as they should, they'll die very quickly. If your raid DPS is good, it'll only be worth putting up one DoT and using your single target attacks on them. I try very hard not to let my DoTs fall off Gormock while attacking the Snobolds, this extra bit of Multi Dot DPS is helpful.
If the Snowbolds land on you, you're actually able to attack them with a few abilities. You can attack with SW:P, DP and SW:D, your instant casts basically. If you try to use VT, MB or MF, odds are you're going to be stunned or interrupted. I tend to use my instant casts and then use Dispersion, using this period of time as a mana regen break. Dispersing also helps lower the damage you take, very useful for helping your Healers conserve their mana for later phases of the fight.
Phase 2 - You've Got Worms!
Ok, this is probably the most complicated phase of the fight. You've got two giant Jormungers to kill, Acidmaw and Dreadscale. Here's the first thing to remember, Acidmaw = Bad Poison and Dreadscale = Helpful Cleansing Fire.
Here's a quick run down. Acidmaw will start out rooted in place, while Dreadscale is mobile. Both spew out nasty breath attacks, so stay behind em. Periodically, both with burrow underground and then hop out in a random spot. At that point, they'll switch which one is Stationary and which one is Mobile. The mobile worm drops down Grobbulus style clouds, so he's being slowly kited. They have to be kept close together though, becuase of two special abilities Paralytic Bite / Spray and Burning Bite / Spray.
So, first off, the worms use their Bite when they're mobile. This will wind up hitting the tank (or a bad DPS that pulls aggro). The spray is used by the stationary Worm. It hits one random raid member and splashes to anybody within 10 yards of that person, so spread out. The Paralytic Spray applies a nasty debuff that slows you down. The slowing effect increases in strength, until you wind up rooted in place. The Burning Spray applies a nasty DoT that hurts everybody within 10 yards of you, this is similar to the Light Bombs on XT. This fire damage clears the Paralytic debuff though.
So, if you get hit by the Paralytic Spray, you need to run towards somebody with the Fire debuff. If you've got the Fire debuff, you need to stay 10 yards away from everybody else, BUT be ready to run towards anybody who gets paralyzed.
One last thing, when one worm dies, the other one becomes enranged and must be DPSed down fast.
So... this is a Phase where a Shadow Priest can really shine. As you might imagine, raid damge tends to be pretty high on this phase. Don't be afraid to toss out PW:S on people who are low on health, I've saved several deaths this way. Keep VE up on both worms, and I'd suggest you try a bit of Multi-DOtting for a nice DPS boost that actualy helps the raid (whiel increasing your VE heals). If somebody messes up, pop your Divine Hymn, it can be a God-Send. Yes you're going to sacrifice a bit of your DPS with these tactics, but your Healers will appreiciate the help (especially while your group is learning the fight).
One last thing to note, and this is important. When they worms burrow underground, they reset their aggro tables. Your DoTs will keep ticking. This means that when they pop back out, you'll probably have agro on both worms. While they're underground, if you pay attention you'll see a trail of debris on the ground. Run away from it if you don't want to risk getting killed =).
Phase 3 - Icehowl the Adorable
Seriously, Yetis look like a stuffed animal more than a raid boss. And as far as the Beasts go, he's a joke. He hits a tank somewhat hard, but not too often. His only raid attack is a cone breath attack, similar to the Giants you fight while clearing Hodir's trash. This isn't a big concernt, so long as you're not terribly unlucky and so long as the raid doesn't clump up too much.
His only tricky ability is that every so often he jumps to the center of the arena and slams everybody to a wall. You'll be stunned along the wall, and while you're stunned pay attention for his Emote. He'll target one raid memmber, and charge at them. When the stun ends, that raid member and anybody near them has to run away fast. If Icehowl hits you, you're gonna instantly die and he'll enrage, causing huge amounts of damage to the tank. If he doesn't hit somebody, he's stunned and will take 100% extra damage for 15 seconds.
Note, this is a % based debuff on the boss, so reapply SW:P. It will most likely have worn off anyway, due to the time spent stunned on the wall, but by reapplying it after you get 5 stacks of Shadow Weaving back up, you can maintain 110% extra damage on SW:P until the next stun. This is a tank & spank aside from that.