Sludgefist was born in the muddy foundation beneath Castle Nathria and now wanders the halls as he awaits orders from Sire Denathrius. His massive footsteps reverberate throughout the castle, announcing his arrival from several rooms away.
The damage received by the boss tank will be dealt to the off-tank with 
Giant Fists. Because of this tanks with high physical mitigation should be the boss tank.
Move out of 
Destructive Stomp
Aim the boss to a pillar for 
Hateful Gaze
Brewmaster a very strong choice of tank for this encounter due to 
Stagger.
[Mythic] DO NOT roll away from your co-tank on Destructive Stomp. You are going to be faster than them and snap your chain.
Vengeance Demon Hunter is a strong choice of tank for this encounter.
If you are the off-tank you can prevent your damage taken with 
Blessing of Protection or 
Divine Shield.
As the vast majority of the damage taken on this encounter is from auto attacks 
Shield Block is very powerful. As a result of this Protection Warrior is a strong choice of tank for this encounter.
Guardian Druid is the strong choice of tank for this encounter. Very high amounts of constant mitigation and a high health pool makes it a good choice here.
Blood Death Knight as of writing are not a very strong tank for this encounter (FOR EARLY PROGRESSION) as the spec relies on taking damage to your health pool and then healing it back up, however as the damage is constant it can become overwhelming at low gear levels.
This is a single phase encounter where the boss will require specific movement and deal progressively increasing amounts of raid damage.
Chain Link - This is one of the main mechanics of the fight where 2 players will be bound together by a chain. They will have a short period of time to find their partner (who will be marked with an arrow above their head), and at any point after this if they move more than 12 yard away from each other 
Shattering Chain will trigger and deal a lethal amount of Physical damage to both players (Should either player survive they will be stunned for 6 seconds).
[Heroic] Chain Link is cast on more players.
[Heroic] 
Chain Slam - The boss will immobilise a random player in the raid and after 4 seconds any player within 7 yards of this player will be dragged towards the boss and take a shared amount of Physical damage. This mechanic will require at least 3/4 people, else deaths will happen.
This mechanic will always go on one of the four furthest players.
Giant Fists - This is the main tank mechanic of the encounter where melee damage done to the active tank will carry through to the nearest player within 5 yards. Both tanks should be on top of each other to prevent other players from being hit.
This will essentially work as two attacks, the auto attack on the initial target, and the same hit on the Giant Fists target.
Destructive Stomp - Twice in each main phase this will be cast. The boss will show a ring around himself and any players within that ring after the 4 second cast will take a large amount of Physical damage and be knocked back. Any player in melee should run out of this. Linked players should move together.
If any pillars are in this area, they will be destroyed.
Colossal Roar - At the start of the fight and roughly every 30 seconds thereafter this will be cast. It pushes all players away from the boss and deals a small amount of damage to the entire raid.
Falling Rubble - Throughout the encounter this will be cast on several players. After a few seconds if anyone is within this area they will take a moderate amount of Physical damage and be stunned for 6 seconds. A 
Stonequake puddle will also spawn in that area which deals a small amount of Physical damage every 0.5 seconds and slows movement speed.
Hateful Gaze - When Sludgefist reaches 100 energy he will mark the tank with this debuff. 6 seconds after the boss will charge towards the tanks location and only stop when he hits an object in the room. Any player caught in the path will likely die.
• If he hits a pillar, this pillar will be destroyed and the boss will be gain 
Destructive Impact and be stunned for 12 seconds. During the stun he will take 100% more damage and deal a small amount of damage to the entire raid. This will also apply a stack of 
Crumbling Foundation to the raid which is a small amount of ticking damage which cannot be removed.
• If he hits the wall it will trigger 
Collapsing Foundation.
This means that if the boss does Hateful Gaze for a 5th time, it's a wipe.
Gruesome Rage - At 30% the boss will enrage dealing 20% more damage and have 20% increased attack speed.
Swing Timer: 1.5s (Curse of Weakness 1.8s)
Brewmaster a very strong choice of tank for this encounter due to Stagger.
[Mythic] DO NOT roll away from your co-tank on Destructive Stomp. You are going to be faster than them and snap your chain.
Vengeance Demon Hunter is a strong choice of tank for this encounter.
If you are the off-tank you can prevent your damage taken with Blessing of Protection or Divine Shield.
As the vast majority of the damage taken on this encounter is from auto attacks Shield Block is very powerful. As a result of this Protection Warrior is a strong choice of tank for this encounter.
Guardian Druid is the strong choice of tank for this encounter. Very high amounts of constant mitigation and a high health pool makes it a good choice here.
Blood Death Knight as of writing are not a very strong tank for this encounter (FOR EARLY PROGRESSION) as the spec relies on taking damage to your health pool and then healing it back up, however as the damage is constant it can become overwhelming at low gear levels.
On Mythic difficulty this fight becomes much more about execution as every mechanic is enhanced in some capacity.
Chain Link - All 20 players in the raid are linked together. This means that raid movement will need to ideally pre-planned and assignments will be required to show how people will move based on who they are linked to. Examples include: Always move to melee if you are linked there, always move to a healer if you are linked to one, always dodge to the middle of the room etc.
Tanks are always linked together.
Chain Slam - If less than 4 players are hit by this ability the boss will enrage, increasing his damage dealt by 100% and attack speed by 60%. This will require 2 groups of chain pairs to soak, the group targeted + 1 more. The Chain Slam will also apply 
Chain Bleed to all players hit, so you will want to keep this strictly to 4 people where possible.
Seismic Shift - Throughout the encounter this is cast where you will take a moderate amount of Physical damage, but also deal the same damage to all players within 4.5 yards. As the distance to spread has reduced to 10 yards this means you do not have much room to move around with.
Tip: Use the rings around you to indicate if you are safe from your link partner.
Fractured Boulder - After charging into a pillar, 4 Fractured Boulders will be broken off and need to be soaked. After they have been soaked they will split into 2 
Fractured Debris zones which need to be soaked also.
If any are not soaked then 
Fractured Impact is triggered which will wipe the raid.
There is a strict pattern of damage events during this encounter, 2 Roars and then a Charge. This repeats 5 times.
For a first kill, I would strongly recommend 5 healing. 4 healing requires a higher amount of execution, should your team be capable of that (or if the boss gets nerfed again) then 4 healing is a good choice.
I won't go into full detail on how to assign your specific healer team needs (however, should you have any questions I'm more than happy to help you work through them in the TankNotes discord). But I will detail below your main goals around assigning the cooldowns.
Tank Soak locations.
How you handle the soaks.
You will want to assign players throughout the encounter to bait chain slams.
You may be suprised when looking through logs that Sludgefist doesn't actually hit that hard in comparison to some other bosses. However your enemy on this encounter is healer attention. The damage is spread across the entire raid so the total amount of healer attention you will receive is much lower than any other encounter.
This does not mean that you need to play really defensively, but to be smarter about how you're playing the encounter.
You know that there are reprieves from direct damage during each Stomp and Charge, take into account when these moments in the fight are and use them to regenerate resources of Charge based abilities/cooldowns/resources (Runes, Shield Block, Judgment, Demon Spikes, Keg Smash). He also has a quite large hitbox so you can often get a melee range ability off whilst you are running out such as Blackout Kick.