Glory of the Dragon Soul Raider

So from what I can gather from reading the titles of these achievements (and the titles alone!) is
that The Dragon Soul raid consists of your usual boss killing, plus a crazy dragon aspect
followed by the Chromatic Champion and the Deck Defender throwing a party involving inordinate amounts of beer pong resulting in feelings of Dizziness, paranoia, and regrettable hand holding & rainbow tasting that will almost certainly be regretted right before midnight.
The Reward: A Lifetime of Regret, custody of an assumedly angry, moody purple dragon plus some dinky daggers if you're a rogue.
Sounds like a Good Time

Here's a summary of how Glory of the Dragon Soul Raider could be planned and executed in 10m. I won't go into strats other than those needed for the achievements; there are a lot of very good guides out there already!

Heroic progression order
It has become clear that it would be a nearly linear progress path. Everything beyond Morchok is way harder, it gets very crispy from Blackhorn onwards. Madness is definetely not easier than Spine, especially after the 15% tendon nerf.

1. 
   
2. Heroic: Morchok
3. 
   
4. Heroic: Ultraxion
5. 
   
6. Heroic: Yor'sahj the Unsleeping
7. 
   
8. Heroic: Warlord Zon'ozz
9. 
   
10. Heroic: Hagara the Stormbinder
11. 
    
12. Heroic: Warmaster Blackhorn
13. 
    
14. Heroic: Spine of Deathwing
15. 
    
16. Heroic: Madness of Deathwing

Normal achievements
It is adviseable to start doing them as soon as possible, or you may need to waste a heroic madness kill/progress ID only to get the achievements later on. A few of them will be easily doable on heroic mode though.

Don't Stand So Close to Me
NHC: Assign 5 groups of 2 to 5 different directions, each consisting of a class with a speed buff (disengage, sprint, blink, teleport, whatever) and one without. Once drawn to the center, the fast classes use their speed skills as soon as possible, so that they end up about 10 y ahead of the slow class. Once at range, there's enough space to spread, no one needs to hug the shards. Certain achievement tracking addons might fire false positive fail warnings. Better just keep an eye on the range meter or look at the Blizz achievement-tracker.
HC: Simply assign five directions beforehand and tank the bosses well apart.

Taste the Rainbow!
NHC: This can be done in multiple kills. A well experienced and geared raid can focus on all combos with ease instead of following the classic killing priority. However, the purple&yellow combo requires better awareness: don't spam heals or shields and use defensive cooldowns. Also, consider just letting all three through on normal mode towards the end of the fight.
HC: It is risky to focus on the achievement, but you can get it in case you're lucky with the last blob combo. When the boss has only a few % left, consider letting all four pass, killing him a few secs later.

Ping Pong Champion
NHC: Pretty straight forward. It will most likely bounce 11 times actually, because the orb spawns near the ranged group. Assign 3 people (2 ranged and 1 melee) with cooldowns for the last 3 bounces. The rest needs to go quite far away to not be accidentally hit by the explosion.
HC: Doable for well geared raids with enough classes which can take a bounce solo (3 at least).

Holding Hands
NHC: Make sure all pets are dismissed or in the center, as they can appearently screw it. Form a line with players every 6-10 yards along the edge of the platform starting from the last inactive crystal thingy, going towards an activated one. Mind to stay away from the activated one, so that it stops casting lightnings on players. Wait for everyone to be in position, before the last person moves towards the active crystal, closing the circuit. Note that the achievement will be awarded immediately and that weird cluttered player positions, or standing too close to each other, can screw it. Make sure that everyone has exactly 2 players within 10y range, one to the left and one to the right.
HC: There's no way but also no need to do it on HC. Just set normal, get the achievement, wipe, switch to heroic, kill the boss. :)

Minutes to Midnight
NHC: This is again a simple one: assign 7 people with a defensive cooldown. If you 2 heal it, you shouldn't see more than 6 HoTs.
HC: Once your DPS is high enough to kill him in 5 HoTs, it is possible. Use external defensive CDs on people without any on their own.

Deck Defender
NHC: Divide the deck in areas and assign players. Everyone within reach should run into the barrage (1 person is enough). During twilight onslaught, have a mobile class like a mage stay approximately in the middle of the deck to backup the barrages that are far away. People will survive the barrage alone, but make sure to avoid the charges or the healers will hate you. High damage output on the drakes makes everything considerably easier; the sooner they die, the fewer barrages!
HC: Hard but possible with fast drake kills, the right classes and a pint of luck.

Maybe He'll Get Dizzy...
NHC: Right after the pull, kill 2 tentacles, turn left. kill 1 tentacle, turn right. Then proceed as normal, only make sure you turn left after the 1st plate, then right after the second. You can kill fewer tentacles in the 1st sequence when you roll twice, but this is just unnecessarily stressful to the healers, due to the beam. You'll still get the achievement if you make him turn more after the sequence.
HC: A bit messy, but possible right after the pull.

Chromatic Champion
NHC: This one has to be done in at least 4 IDs, 8 if your roster is larger than 10 people. Here's a suggestion of killing orders, starting from the easiest one. The first three shouldn't be much of an issue for experienced and geared raids - the last one is clearly harder.

1. green - red - yellow - blue
2. 
   
3. red - green - yellow - blue
4. 
   
5. yellow - red - green - blue
6. 
   
7. blue - green - red - yellow

HC: Pretty surely no one will ever want to try any other than the easiest combo until MoP, which is always with green first. :) So get started on this achievement as soon as you can.

Have fun and good luck!

Reward for this achievement is [item=77068], according to the official database.

Strangely enough, it requires killing Deathwing on Heroic difficulty, something that didn't happen on Firelands or ICC.