Relevant Talents used:

Angelic Bulwark
Divine Insight

Relevant Glyphs used:
Holy Nova
Dark Binding
Optional (I used reflective shield)

iLvl: 504
Chimaeron attacks slowly. But every attack deals anywhere between 150k - 250k damage. Every third attack is a double strike, which means he attacks twice in a row.
However as long as players remain above 10k health, attacks will not kill them, but bring them down to 1 hp. So as long as the players gain over or remain above 10k health between each attack, they will not die. The boss casts a tank debuff called Break, which at max stacks reduces healing taken by 60%. From a soloing perspective, it can be assumed that this debuff is up 100% time at max stacks.

Finkle's Buff:
While this buff is active, players above 10k health can absorb a fatal blow, leaving them at 1 health.

Power Word: Shield:
The key survival spell of the fight. It is not affected by Break. When this spell is cast, the amount absorbed per boss hit is not the actual strength of the hit itself, but the amount required to take you down to 1 health. For example if a player is on 10,001 health, a blow from the boss would bring them down to 1 health, hence dealing 10k damage. With PW:Shield up, this 10k damage is simply absorbed, which means they remain on 10,001 health. This way, a shield that can absorb 70k damage can absorb 7 hits. Obviously the higher the player's health, the more damage is dealt to bring down to 1 health, hence the lesser amount of hits the shield can absorb. Hence obviously lesser health is preferred (but not below 10k). Hence any abilities that rapidly regens health, such as Desperate Prayer, Flash Heal, T6 talents, Devouring Plague are not used here. Prayer of Mending is useful though, and this will be covered shortly. Shields cast by players with under 13k health should not break from damage, only expire from duration.

Dealing with Double Strike:
As mentioned earlier, a double strike is 2 hits in a row. When unmitigated, the first hit will bring a player down to 1 health, immediately followed by the second hit which kills the player without any chance to heal back up. When PW:Shield is up, this simply removes 2 hits worth absorbs from the shield. There will be times or circumstances when the shield breaks or has its duration expire just as a double strike comes in. As mentioned earlier, taking a double strike unmitigated is fatal. Therefore an extra layer of insurance is necessary, and Prayer of Mending is perfect for this. Firstly it is not affected by healing de/buffs so Break will not affect it. Secondly it allows to live through a double strike unmitigated. The first hit brings down to 1 hp, PoM kicks in before the second hit, hence allowing the player to survive the second hit. In situations where PW:Shield survives the first hit, but breaks on the second, and PoM kicks in, health level will likely become 20k+, which is undesired (too high). Hence simply take the next hit unmitigated and Holy Nova back to ~10k.

Feud:
The boss occasionally casts Feud for 30 seconds. During this time, Finkle's buff will be turned off. And the raid must start healing through the raid damage. This raid damage does not seemed to be aimed at tanks due to their Break debuff. Hence from a soloing perspective, Feud does nothing. Free 30s of DPS.

Phase 2:
Starts when boss reaches 20%.
Do not hit this phase during Feud as the boss will immediately start to melee attack and you have no Finkle's buff to survive them. During this phase an extra debuff applies that reduces healing taken by 99%. So not even holy nova works now.. But PoM still works since its unaffected by healing de/buffs. Phase 2 is basically treated the same as Phase 1.