Some friends of mine starting up an old guild were having similar issues, I sent them this.
Festergut 3rd Inhale
Tank Rotation and CD's:
During the 3rd Inhale the current tank must chain cool downs (personal or external) for the entire duration, or they will die. The damage is just to great.
Tank 1 - Pulls, holds the boss for 9 stacks
Tank 2- Taunts as soon as Tank 1 gets 9 stacks. If Tank 1 hits 10 stacks its an instant raid wipe.
Tank 2- Waits for Festergut to cast his 3rd Inhale (this happens shortly after the tank swap). When the 3rd Inhale has 2 seconds left to finish on its cast, I hit Last Stand and Enrage Regeneration. 2 seconds before Last Stands ends I hit Shield Wall.
**I am not sure what the other classes abilities are called, I am assuming we all have similar ones. If needed an external CD can be used such as Pain Suppression or Guardian Spirit. If you mess up the timing you can also use a trinket or 2 at the end to ride out the rest of the 3rd Inhale.
Since the DPS check on 10 man is much lighter, it is recommended to use 3 healers to make the fight easier.
0 Inhale(start) -At the start 1 healer is on the tank and 2 are on the raid (due to the gas damage from the room being full at the start).
1st Inhale - Same as above.
2nd Inhale - After his second Inhale 2 healers should be on the tank and 1 on the raid (as the raid damage is lighter with less gas in the room).
3rd Inhale - At his 3rd Inhale all healers should be on the current tank (as all gas is cleared from the room and no one should be taking damage, aside from the one vial gas target at ranged, have one healer pop a few heals or hots on them).
Now the above was for the 10 man, but the tank rotations and CD's are identical on the 10/25. For the healers on 25 the same situation applies, just the number of healers changes. For that I cannot give you specific numbers since I don't recall what we use, I believe 6 total.
There is something so appealing about backhanding someone across the face with a shield.