The number 1 thing that all Healers need to keep in mind during phase 3 is Harvest Soul.

Attempts to harvest the target's soul, dealing 7500 Shadow damage per second for 6 sec. If the target is still alive after the channel is completed, the target's soul will be transfered into Frostmourne to be devoured. Channeled. 15,000/sec on 25-player.
Note that in Lich King 25 Harvest soul ticks for 15k per second, making it much harder to heal. We'll setup a CD rotation for the Harvest Souls. They come in 70 second intervals, so we should have at least the first 4 covered.
1st Harvest Soul, Beholdeth - Pain Suppresion.
2nd Harvest Soul, Majikat or Kissz - Guardian Spirit.
3rd Harvest Soul, Chosin - Divine Sacrifice.
4th Harvest Soul, Turalion - Divine Sacrifice.
Melee DPS
After the transition from Phase 2 to 3, stay with the Off Tank (but be extremely careful about your positioning so that you do not get breathed on by the Raging Spirits), and finish off the adds.
Keep in mind the 2 ways you can die during this phase.
1st. Not spreading out for Defile. Watch your positioning, keep your eye on the Defile timer - pay attention when we call Defile out on vent and spread out.
2nd. Not being aware of the Vile Spirits when they are descending onto the raid. DKs, try death gripping the Vile Spirits down into the melee clump before they become "active", try to see if they will still explode prematurely - if not we can easily get rid of 3 Vile Spirits before they become active. For now we will grip them down one at a time, first Manbearbowen - if the Vile Spirits do explode when they are gripped, wait until the healers catch up with the healing before gripping a second Vile Spirit into the melee.
Ranged DPS
Your main priority in Phase 3 is to DPS down as many Vile Spirits as you can before they descend into the raid. Warlocks spam seeds, Shadow Priests make sure you are glyphed for Mind Flay, Mages and Hunters single target down as many as you can. Note that the Vile Spirits are kiteable as they descend into the raid, kite whichever Vile Spirit is focused on you away from the raid. Make sure to be spread out, especially away from healers but most notably the off tank (Lukelee) who will be taunting as many Vile Spirits onto him as possible.
Your priority is Vile Spirits first, then Lich King second.
Harvest Soul - Frostmourne room.
Every 70 seconds Arthas will port one person into the Frostmourne room. If you are the person who gets ported inside the Frostmourne room here is what you should expect. Inside the room will be Terenas and a mob named a Spirit Warden. The Spirit Warden will be channeling a spell called Soul Rip on Terenas.
If you are DPS - interrupt the channel, you can use a stun, a fear, counterspell, etc. Any form of CC will interrupt the channel. After interrupting the channel, DPS don the Spirit Warden.
If you are a Healer - if you cannot interrupt the channel, the spell that the Spirit Warden is casting is a dispellable Magic effect. If you are a healer capable of dispelling Magic debuffs, cleanse Terenas right away. After cleansing heal Terenas, the higher HP he has, the more damage he will do to the Spirit Warden.
Once the Spirit Warden is dead, you will be ported out of the room.
In a nutshell:
This final phase while easier than phase 2 is still significantly difficult. Don't lose focus. Keep your calm. This is primarily a Stay Alive phase. As long as you keep spreading out for defile, as long as you focus on Vile Spirits, as long as you heal Harvest Soul - it's a win. Do not panic or try to do more than your assignment! Keep calm, do your job, stay alive, and the kill is ours.
Ranged DPS play conservatively, make sure you are always spread out before DPSing. Always make sure that you are in range of at least 3 or 4 healers in Group 5 during this phase.
Melee DPS play conservatively, make sure you are paying attention to the Defile timer and spread out accordingly. Always make sure that you are in range of at least 3 or 4 healers in Group 5 during this phase.
Healers, as always you are carrying the raid. Do not ignore Harvest Soul. This is the #1 way a raid wipes during Phase 3. If the person focused by Harvest Soul dies, Arthas gains a 100% damage buff which will quickly make short work of the tank. All healers need to setup their raid frames to track this debuff. When it is called and someone is affected by this ability, drop whatever you're doing and cast your quickest heal on that person immediately. The DPS on target in 25 man is very unforgiving. If that person does not receive at least 1 or 2 heals within 2 seconds, they will die.
Lastly...
We've had our ups and downs as a guild over the past year. On multiple occasions, at every tier, we've come back from the edge of dissolution only to do better and outdo ourselves. To our core, congratulate yourselves because you've kept this team alive through the thick and thin; to our new recruits, you are the new breath of life this guild has needed and we couldn't do this without you - without each other, none of us would be here at the last milestone of this expansion.
This is the finish line.
Let's remind ourselves of the cold suck hinterlands of PUGs and realize the strength we have as a team. PUGs don't believe in each other, and they cut each other short. They expect other people to carry their slack and they get pissed at the slack they have to carry. But we're a team. We wipe it, we do it again, if we regress, we learn to do it better, if we progress we still learn to do it better; at the end we do it perfectly and we win.
Focus you damn scrubs,
Awesome Possum,
Absolutely Gorgeous,
Jesus Christ You Retards,
I love the way your mom smells in the morning,
Holy Fucking Shit We're Gonna Do it!
Whip it out and Slap it!
Fuck Mother Fucking Yes!