The correct way to fight this battle is to watch out for and move accordingly to the following abilities:
Barrel Roll: Throughout the encounter, Deathwing tries to throw players from his back when he senses that they are all standing on the same side of his spine. During a barrel roll, all players and other creatures not attached to his back are thrown off.
Elementium Reinforced Plates: The glancing strike from the Dragon Soul has destroyed one of the large armor plates on Deathwing's back and loosened another three. All of these plates must be removed if Thrall is to have a chance to get a clear shot.
Burning Tendons: Burning Tendons are exposed when one of Deathwing's armor plates is pried up. Destroying these fibrous strands is the key to removing an armor plate.
Seal Armor Breach: When an armor plate is pried up, the Burning Tendons rapidly pull the plate closed, protecting the tendons from further damage and preventing the plate from flying off.
Deathwing's Immune System: The creatures that comprise Deathwing's Immune System emerge from the holes in his back left by torn off armor plates. Deathwing defends himself with increasing intensity as more plates are torn off.
Grasping Tendrils: These tendrils sprout from holes in Deathwing's back that aren't currently occupied by Corruption tentacles. Players that wander too close will be grasped, reducing their movement speed by -50% and inflicting 15000 Fire damage every 0 sec. until they move away. This effect prevents players from being thrown off Deathwing's back.
Corruption: These tentacles are dramatic physical manifestations of the Old God Corruption that runs rampant through Deathwing's body. They are the first to emerge from the holes in his back left by armor plates, and they seal the wound completely, preventing any other creatures from emerging from it.
Searing Plasma: Coats the victim in the searing blood of Deathwing. The thick blood will absorb up to 300000 healing done to the target and will cause the victim to cough up blood, periodically inflicting 10000 Physical damage.
Fiery Grip: Grips victims with a whip-like cord of plasma, stunning them for up to 30 sec and inflicting 50000 Fire damage every 5 sec. The corruption must channel to maintain this effect, and it may be broken by inflicting significant damage to the tentacle. This effect prevents players from being thrown off Deathwing's back.
Hideous Amalgamation: These unstable creatures are a patchwork of Elementium Armor fragments and pieces of the former Dragon's body held together by his molten blood.
Absorb Blood: Absorbs nearby Corrupted Blood residue. The Amalgamation grows more unstable with each Residue absorbed, increasing its damage by 10% and attack speed by 10%. At stacks it will become superheated.
Superheated Nucleus: The core of the Amalgamation becomes critically unstable, causing it to inflict 15000 Fire damage to all enemies every 3 sec. If it is destroyed in this state it will trigger a Nuclear Blast.
Nuclear Blast: The superheated nucleus of the Amalgamation triggers a massive explosion, inflicting 500000 Fire damage to targets within 10 yds. This blast is powerful enough to pry up one of Deathwing's Elementium plates if it is within range.
Degradation: Destroyed Amalgamations degrade the maximum health of all enemy targets by -6%. This effect occurs regardless of the state of the nucleus and stacks up to $106005u times.
Blood Corruption: Death: Deathwing's corruption courses through your veins. This corruption will take hold if it is not removed quickly, infecting the player with the Blood of Deathwing. When dispelled this effect jumps to a new target and can mutate into Blood Corruption: Earth.
Blood of Deathwing: The blood of Deathwing explodes violently from your veins, inflicting 875000 Fire damage to you and several other players.
Blood Corruption: Earth: A shadow of Neltharion courses through your veins. This corruption will take hold if it is not removed quickly, infecting the player with the Blood of Neltharion. When dispelled this effect jumps to a new target and can mutate into Blood Corruption: Death.
Blood of Neltharion: The barest hint of a shadow of the former Earth-Warder suffuses your blood. Damage taken from all sources is reduced by -10%. This effect can stack up to times.
Corrupted Blood: These living globs of Deathwing's blood appear fragile, but leave behind an indestructible residue when killed.
Burst: Corrupted Blood explodes when destroyed, inflicting 25000 Fire damage to nearby enemies.
Residue: This indestructible residue is left behind when a Corrupted Blood is destroyed. It slowly creeps toward the nearest hole in Deathwing's Back where it will be reconstituted into a new Corrupted Blood.