How do you protect tanks on Festergut?

Does your raid have a ret paladin? If you do, he/she can place Hand of Sacrifice, and thus soften the impact of hits on the tank's health. Now, of course the paladin would need to be healed too, but chain heals/another set of HoTs/his own HL spams could take care of that.

The Gastric Bloat is nature damage, the Pungent Blight shadow, I believe his hits are normal physical damage. Make sure Resistance buffs are up (Shadow from a priest/paladin, Nature from a shaman/hunter) - while resisted damage is a bit of an RNG lottery, it will certainly help through the fight. Also keep in mind that your tanks should use a potion per fight: either a Nature Protection, Shadow Protection or Invulnerability Potion, again, depending on where you feel the weak spot of your raid is.

Also, remember that tanks have more than one cooldown available to them. I don't play warriors or DKs, but even I know that warriors have Shield Wall and Last Stand (at the very least) and DKs have Icebound Fortitude and... huh... well, they must have something else. Add to that at least one if not two trinkets (dodge, armor on use) and that could help you get through the 4th inhale.

Ok, this is a relatively straight-forward problem. There's two separate issues you need to avoid after the third inhale:

1. You need to prevent the tank from getting insta-gibbed. (death without a chance for a heal)

2. You need to keep maximum heals flowing to the tank.

You actually have a decent comp for this. The only truly "better" third healer you can have for that comp is a Disc Priest. This is because the shields of the Disc Priest can really help smooth out some of the damage in that portion of the fight. However, there's absolutely nothing deficient about the composition you have.

Let's talk about these two issues separately starting with the first one.

Avoiding Insta-Gibs
The goal here is to minimize incoming tank spike. This is a relatively straight-forward exercise as there are only two ways to do this: better gear and cooldowns. Whichever of your two tanks is the absolutely best geared should tank second. After a number of raids you should have an idea who is the best geared of your tanks. I tend to believe that Druids because of high dodge, armor, and stamina and Paladins with Ardent Defender tend to be the better of the tanks for tanking during this phase, but it's not a necessity.

As you've stated have your tank who is taunting wait until the third inhale to start using CD's and then blow them in a chain. They won't be tanking again in third phase (the mechanics of the fight are such that the 2nd tank will be tanking during that portion of the fight) so the length of the CD's doesn't matter. For example, the Warrior can start with Shield Block into Shield Wall into Last Stand for 42s of decreased damage of various degrees. The Death Knight can similarly can chain Icebound Fortitude into Unbreakable Armor for 32s of decreased damage and also use Death Pact to help mitigate burst. Tanks could also have Indestructible Potion and possibly depending on composition have Fel Healthstone.

Those are the long-length cooldowns. In addition to those above, you simply MUST have the following ALWAYS active on the tanks in this encounter.

• Thunder Clap or Icy Touch (whichever is talented to 20% attack speed decrease) will drastically help with the burst damage after the third breath.
• Demoralizing Shout (talented) also is a tricky spell in that it's not clear exactly what it accomplishes but it is vital. It lowers the damage of the boss by 10-25% (I've heard 15% thrown around most often).
• Ancestral Healing is applied by the Shaman on critical spells. We'll get to how to heal the tank in the second part of the post, but suffice it to say it should ALWAYS be on the tanks after 3 inhales. All the tough damage is physical so it's 10% less damage coming in.

The combination of all these effects should prevent almost all occurrences of tanks getting unhealable damage spikes. However, it's still possible that they take heavy damage with a bad avoidance string or potential parry hasting. There's not much you can do here than curse the almighty gods of RNG and attempt the fight again.

Maximum Healing It sounds like a lot of damage that's coming in to the tank in that phase, and it is, but you have to remember the key point of the fight of Festergut that is supposed to be hard/fun for the healers: the fight changes from a heavy AoE Heals fight to a heavy Tank Heals fight because of the inhale mechanic. As the 2nd and 3rd inhales occur, the raid is taking essentially no damage. So, what I would do with your 3 healers (2 druids, 1 shaman) is to put the shaman on the tank full-time, while 1 druid is on full-time raid healing, and the other is the "flex" healer.

Side-note: make sure you have as many of your healers as possible (and at least all of your tank healers) inside of melee range to avoid them getting incapacitated by Vile Gas. If your healers get hit by this after 3 inhales, the tank will almost surely die.

At 0 and 1 inhales, the tank damage is light but the raid damage is severe. The Shaman should keep Earth Shield on the tank while alternating between Glyphed Lesser Healing Wave and Chain Heal on the tank depending on tank spike. If you can get away with always using Chain Heal, do that, because it will keep the healers and melee topped off on health as well. You use Lesser Healing Wave instead of Healing Wave because it's by far more mana efficient and you can afford then to always have a tank receiving heals. The fight is very mana intensive and therefore you want to use the most mana-efficient spamming you can do. At this point in the fight, the Druids are doing what Druids do best, Rejuvenation blanketing.

At 2 inhales, the tank is taking some big spike. The Shaman is now focusing almost solely on keeping the tank alive and using Chain Heal very infrequently whenever the tank is completely topped off. Now, one of the druids, the "flex" healer will switch to the tank. His job is to keep all of his HoTs on the tank (Rejuvenation, Wild Growth, Regrowth, possibly even Lifebloom) while using Swiftmend, Nature's Swiftness, and Nourish as necessary to keep direct heals flowing into the tank. Somewhere during the 2nd inhale, the tank swap will happen. Make sure the swap is communicated clearly to the healers and that the healers begin to pre-heal the second tank to insure the tank doesn't kersplat as soon as they taunt.

At 3 inhales, now all three healers are on the tank. The raid will take minimal damage for which one druid should have no problems keeping up. However, all spare GCD's go to the tank. This is the most crucial part of the fight, and it's when you use all the CD's I mentioned above. For the Shaman, you keep Riptide on the tank, Earth Shield on the tank, and you spam Lesser Healing Wave like you have no tomorrow. Similarly, both Druids keep all HoT's rolling on the tank.

Riptide can tick for like ~700-1.2k, Rejuvenation for like 2-4k, Earth Shield for 4-6k, LHW for 6-11k, Earthliving for like 700-1.1k, Regrowth for like 1k+, Wild Growth for like 800+, Nourish for 8-12k. When you add up all the totals of healing coming in, it's far more substantial than you realize. Just make sure all the healers are SPAMMING the tanks. You can mana up afterwards. If you have reasonably good RNG, the tank will live to the exhale. Then IMMEDIATELY switch back to covering the raid because raid healing is suddenly huge again.