I listed every achievement that must be completed in order to get this meta-achievement, even including ones that require you to kill bosses or complete the raid dungeon, don't flame me for that please. While I do not have this achievement completed I do have most of it done and this is how I did it within my raid (Sartharion + 3 Drakes sucks)
Besting the Black Dragonflight
Criteria: Defeat Sartharion the Onyx Guardian on Normal Difficulty.
How to: See Criteria. Recommended 2 Tanks, 2-3 Healers, 5-6 DPS.
Less Is More
Criteria: Defeat Sartharion the Onyx Guardian and the Twilight Drakes with fewer than 9 on Normal Difficulty.
How to: 8 Players or less basically. Recommended 2 Tanks, 2 Healers, 4 DPS in decent gear.
The Arachnid Quarter
Criteria: Defeat the bosses of The Arachnid Quarter of Naxxramas on Normal Difficulty.
How to: See Criteria. Recommended 2 Tanks, 2-3 Healers, 5-6 DPS.
The Construct Quarter
Criteria: Defeat the bosses of The Construct Quarter of Naxxramas on Normal Difficulty.
How to: See Criteria. Recommended 2 Tanks, 2-3 Healers, 5-6 DPS.
The Plague Quarter
Criteria: Defeat the bosses of The Plague Quarter of Naxxramas on Normal Difficulty.
How to: See Criteria. Recommended 2 Tanks, 2-3 Healers, 5-6 DPS.
The Military Quarter
Criteria: Defeat the bosses of The Military Quarter of Naxxramas on Normal Difficulty.
How to: See Criteria. Recommended 2 Tanks, 2-3 Healers, 5-6 DPS.
Sapphiron's Demise
Criteria: Defeat Sapphiron on Normal Difficulty in Naxxramas.
How to: See Criteria. Recommended 2 Tanks, 2-3 Healers, 5-6 DPS.
Kel'Thuzad's Defeat
Criteria: Defeat Kel'Thuzad on Normal Difficulty in Naxxramas.
How to: See Criteria. Recommended 2 Tanks, 2-3 Healers, 5-6 DPS.
The Fall of Naxxramas
Criteria: Defeat every boss in Naxxramas on Normal Difficulty.
How to: See Criteria. Recommended 2 Tanks, 2-3 Healers, 5-6 DPS.
The Dedicated Few
Criteria: Defeat the bosses of Naxxramas on Normal Difficulty with less than 9 people in the zone.
How to: See Criteria. Recommended 2 Tanks, 2 Healers, 4 DPS in decent gear.
Arachnophobia
Criteria: Defeat Maexxna in Naxxramas within 20 minutes of Anub'Rekhan's death on Normal Difficulty.
How to: Normal Raid group composition. Kill Anub'Rekhan the same way you normally would, make sure that no one dies. Don't sweat Master Looting, just set it to Group Loot and do Need/Greed that way your not wasting time on loot. On the way to Grand Widow Faerlina do 2-3 packs at a time and AoE them down, a good tank will not die if you have 3 healers. The trash infront of Faerlina can be all pulled at once, Blood Elves can Arcane Torrent the ranged ones to make it easier to AoE. While doing this achievement you might as well do "Momma Said Knock You Out" since it's going to be the fastest way to kill Grand Widow Faerlina. Again, double pull all the way to Maexxna using AoE. You should have roughly 3-5 minutes remaining on the timer, so just burn hard. Bloodlust should be up and used on both of the last 2 bosses.
Make Quick Werk Of Him
Criteria: Defeat Patchwerk in Naxxramas on Normal Difficulty in 3 minutes or less.
How to: This is simply put a DPS race. 2 Tanks and 2 Healers, 6 very good DPS. Patchwerk has 4 Million HP and you have 180 seconds to kill him. Math says 22,222 DPS is required to meet this goal so that means each DPS needs to do 3700 DPS if the tanks did 0 damage.
Lets say the tanks did 1500 each (kinda low), then the 6 DPS would need to each do 3200 DPS. This is very realistic with Bloodlust and high DPS players.
The Safety Dance
Criteria: Defeat Heigan the Unclean in Naxxramas on Normal Difficulty without anyone in the raid dying.
How to: You should know the fight if you are reading this. It basically requires no one to be slow or lagging to complete. The only reason someone will die is because they fail at Phase 2 aka "The Safety Dance". Do not use Aspect of the Pack to increase your speed. You won't die from one hit, but if you do get hit you will be dazed and most certainly take that second hit. Death Knight's Unholy Aura is helpful though.
Momma Said Knock You Out
Criteria: Defeat Grand Widow Faerlina in Naxxramas on Normal Difficulty without dispelling frenzy.
How to: Have the best tank on Faerlina and the other tank on the adds. Keep them seperated and burn Faerlina as much as possible. I've tried killing the adds off the start and did not get the achievement so it is advised to just leave them up and kill Faerlina. A decent tank will not get hit all that hard and the only damage should really be on the 2 tanks pending people can dodge Rain of Fire.
Shocking!
Criteria: Defeat Thaddius in Naxxramas on Normal Difficulty without anyone in the raid crossing the negative and positive charges.
How to: The best way to do this is to utilize "The Box Strat". It requires each individual person to watch his/her own charge and his/her own charge only. Designated positions for the initial Polarity Shift are spots 1 and 3, Positive charges run to 1, Negative charges run to 3. From here, if your charge changes you run vertically (up and down) if it stays the same you run horizontally (left and right). This makes it so that no one will ever cross, but they can be dumb and forget which way to move. Example of this is: You are positively charged initially, you run to spot 1. Polarity Shift occurs, you stay positive so you run to spot 2. Polarity Shift occurs again, you become negative, you then run to spot 3. Below is a diagram.

Subtraction
Criteria: Defeat Thaddius in Naxxramas on Normal Difficulty with less than 9 people.
How to: Do it the same way as Shocking! using 2 tanks, 2 healers, and 4 DPS.
Spore Loser
Criteria: Defeat Loatheb in Naxxramas on Normal Difficulty without killing any spores.
How to: Same tactics as you normally would do but you want to burn him in roughly the same time. 6.7 Million HP to be burned by 1 Tank, 2 Healers, and 7 DPS. This requires 22,333 raid DPS to complete in 5 minutes (the "enrage" og Inevitable Doom). Basically, if you can do a 3 minute Patchwerk you can do this.
And They Would All Go Down Together
Criteria: Defeat the 4 Horsemen in Naxxramas on Normal Difficulty, ensuring that they all die within 15 seconds of each other.
How to: Bring 2 tanks, 2-3 healers and 2 people willing to range tank. Do the encounter as normal but split your 5-6 DPS to each corner. To make healing a little bit easier stack 3 DPS, preferably melee, in the front so that Thane Kor'Thazz' Meteor doesn't hit so hard (13775-15225 damage split between anyone in an 8yd radius). Put ranged DPS in the back and have them switch back and forth after roughly 3 Marks. Communicate and rotate a few DPS around as needed keeping in mind that 1 person must always be within melee of the Horsemen or they use an ultimate ability that will wipe you.
The Hundred Club
Criteria: Defeat Sapphiron on Normal Difficulty in Naxxramas without any member of the raid having a frost resist value over 100.
How to: See Criteria. The Frost Aura really doesn't tick for all that much. Bring 3 healers if you need to.
Just Can't Get Enough
Criteria: Defeat Kel'Thuzad on Normal Difficulty in Naxxramas while killing at least 18 abominations in his chamber.
How to:You can pull many waves early in the fight and AoE them down since mobs don't come that fast in the early goings. 2-3 full pulls on Abom sections should get it in combination with the normal Aboms that are sent at you. It does become mana intensive though so make sure you can alleviate that (Mana Tide, Evocation, Dispersion, Replenishment buff).
The Undying
Criteria: Within on raid lockout period, defeat every boss in Naxxramas on Normal Difficulty without allowing any raid member to die during any of the boss encounters.
How to: Just as it says. Players may die on trash but not on bosses. The biggest problems you will have here are Heigan, Thaddius, and Sapphiron. Good luck!
The Spellweaver's Downfall
Criteria: Defeat Malygos on Normal Difficulty
How to: See Criteria.
You Don't Have An Eternity
Criteria: Defeat Malygos in 5 minutes or less on Normal Difficulty.
How to: Malygos has 6.9 Million HP and takes flight at 50% with a 20 second speach. Your goal is to burn Malygos to 50% in 2 minutes (28750 raid DPS) , complete phase 2 by 3 minutes 30
seconds, and kill him by 5 minutes obviously. To do this you must ensure all Sparks are stacked at all times possible and not use Bloodlust/Heroism until 52-53%. This is key to getting the achievement! It is possible to burn Malygos during his speach before phase 2 and this is the crucial part. Roughly 30-35% is how much you want him to be at before you enter phase 2 with a few seconds left on your Bloodlust/Heroism. It is realistic because you can get a triple stack of sparks (187.5% increased damage). To finish off 35% in 1.5 minutes is pretty hasty but here is the trick! Stack Flame Spike twice immediately and use Engulf in Flames, immediately restacking Flame Spike twice. Wait till ~75-80 energy and do EiF then FSx2. Rinse and repeat this to have huge stacks for huge damage. In case you are targeted by Surge of Power you will have 2 combo points so use Flame Shield then Flame Spike and immediately reapply EiF so as to not lose your ticks. 2 Healers are all that is required for phase 3.
A Poke In The Eye
Criteria: Defeat Malygos with fewer than 9 on Normal Difficulty.
How to: Bring 1 Tank, 2 Healers, and 5 DPS.
Denyin' the Scion
Criteria: Deliver a killing blow to a Scion of Eternity while riding on a hover disk on Normal Difficulty.
How to: Basically as it says, when a Lord dies hop on the disk and make sure you get the killing blow on a Scion of Eternity.
Gonna Go When the Volcano Blows
Criteria: Defeat Sarthation the Onyx Guardian on Normal Difficulty without getting hit by Lava Strike.
How to: The waves that he releases are not this, it is the fire balls that land on his platform throughout the entire encounter and come sporadically at the end. They have a shadow on the ground for a split second before they land and you have to be standing in that shadow to take the damage, so just don't stand there. Easiest for a tank.
Twilight Assist
Criteria: With at least one Twilight Drake still alive, engage and defeat Sarthation the Onyx Guardian on Normal Difficulty.
How to: Probably easiest to leave Vesperon up, he only does a 25% HP cut and easiest to burn.
Twilight Duo
Criteria: With at least two Twilight Drakes still alive, engage and defeat Sarthation the Onyx Guardian on Normal Difficulty.
How to: Leave Vesperon and Tenebron up. Vesperon is summoned first and then Tenebron. Focus on Vesperon's add in the Twilight Realm and then burn Vesperon. For Tenebron DPS him hard the whole way and let the OT pick up the whelps when they hatch, AoE them down ASAP.
The Twilight Zone
Criteria: With all three Twilight Drakes still alive, engage and defeat Sarthation the Onyx Guardian on Normal Difficulty.
How to: The order in which they appear is Vesperon, Shadron, then Tenebron. Sarthation gains a buff increasing his and the drakes HP by 25%. This becomes very mana intensive and difficult to heal through if you don't burn the drakes fast. Apply the same tactics for Twilight Duo but when Shadron lands and summons his portal put all DPS and an OT in there and burn the add, you should be able to do it fast enough before your tank dies, if not put a healer down there for good measure. If there was a time to bloodlust, it's for Shadron. Good luck, this is the hardest achievement in the game.