Flu Shot Shortage (25 player)

After every 4th Inhale Blight, Festergut casts Pungent Blight, which deals roughly 45k shadow damage.

Normally in the fight, Gas Spores spawn, and you use them to spread the buff Inoculated until you have 75% shadow damage resistance (3 Stacks) to the Pungent Blight attack. This achievement, requires that you do not have 3 Stacks.

In order do that, you need to make sure everyone has only TWO (2) stacks of Inoculated, this cuts the damage of the Pungent Blight by 50% instead of 75%. Even though it's a 50% reduction, you will still take heavy damage, so it's recommended that you use a damage reducing cooldown right before he casts Pungent Blight:

Druids - Barkskin
Rogues - Feint (CONFIRMED THAT THIS WORKS)
Paladins - Bubble
Priests - Shield
Death Knights - Icebound Fortitude + Anti-magic Shell
Warriors - Switch to defensive stance + put on shield and shield wall.
Warlocks - Shadow Ward
Mage - Ice Block
Hunters and Shamans don't have any damage reducing cooldowns that I'm aware of, they'll need to be shielded with Power Word: Shield from a priest.

It's recommended that you kill Festergut before the 2nd Pungent Blight because most of your damage reducing cooldowns won't be back up again.

Easy solo.
Straight burn and you'll be fine.
i639 Shadow Priest.

Some number-crunching for the 25-man version:

Pungent Blight makes a HUGE leap in damage as expected of 25-man raids in comparison to 10-mans, and reveals some interesting things. The range this time is 63.375 to 66,625 shadow damage when it is unmitigated by anything. Mitigated by only 2-stack Inoculated, this drops down to a range roughly between 31,688 and 33,313 damage. Even with a shadow resistance aura/buff in place, most non-tank people will barely survive this without a cooldown, if they survive at all, and will certainly be at the mercy of quick 3k ticks from the fully restored gaseous blight almost immediately. Assuming that one's cooldowns will not always be available to them around the time Pungent Blight hits, some other measures may need to be taken in order to ensure survival, like possibly placing extra shadow resistance on gear or equipping something with higher stamina.

I'm expecting something between 26k-29k for people relying solely on Shadow Protection/Aura of Shadow Resistance on the 25-man encounter.