Power Ascended

This achievement (and the class mount questline) allows you to purchase a set of items depending on your class:

Death Knight (Blood): [npc=119498] from Amal'thazad for 1000 [currency=1220]
Death Knight (Frost): [npc=119499] from Amal'thazad for 1000 [currency=1220]
Death Knight (Unholy): [npc=119500] from Amal'thazad for 1000 [currency=1220]

Demon Hunter: [item=147537] from Falara Nightsong for 1000 [currency=1220]

Hunter (Beast mastery): [item=147580] from [npc=100661] for 1000 [currency=1220]
Hunter (Marksmanship): [item=142228] from [npc=100661] for 1000 [currency=1220]
Hunter (Survival): [item=142226] from [npc=100661] for 1000 [currency=1220]

Mage: [item=147832] from [npc=103169] for 1000 [currency=1220]

Monk: [item=147542] from [npc=99154] for 1000 [currency=1220]

Paladin (Holy): [item=143505] from [npc=99976] for 1000 [currency=1220]
Paladin (Retribution): [item=143503] from [npc=99976] for 1000 [currency=1220]
Paladin (Protection): [item=143504] from [npc=99976] for 1000 [currency=1220]

Rogue (Assassination): [item=143492] from [npc=121282] for 1000 [currency=1220]
Rogue (Outlaw): [item=143490] from [npc=121282] for 1000 [currency=1220]
Rogue (Subtlety): [item=143491] from [npc=121282] for 1000 [currency=1220]
Rogue: [item=143679] (by completing quest Fit For a Pirate

Warlock: [item=143637] from [npc=101097] for 1000 [currency=1220]

Yes. It is still possible to get the legion class mounts in 8.0. I have done it on my newly leveled priest (from 1), and I am currently doing it on my Paladin whom I boosted to 110. If you're stuck: you need to complete your class hall campaign, breaching the tomb achievement, AND one of the "specialization" quests from The Violet Citadel in Dalaran to complete power ascended. You then return to Broken Shore - Deliverance Point and there will be a new NPC there with a quest for you to do in your class hall.

[Edit, in 7.3.0 this requirement seems to have been hotfixed away. Getting the power ascended achievement no longer requires a questline]

For those in 7.3 that come here wondering why they have concordance unlocked and put a point into it, but did not receive the power ascended achievement and are unable to buy their power ascended items:
You have to complete the questline that starts on the broken shore and ends with "a gift from the six" (For a guide that shows all the class and specialization specific questlines, see http://www.wowhead.com/empowered-artifact-traits-in-patch-7-2). Even though it is no longer required to unlock additional traits, it is still a requirement for power ascended and thus for obtaining the extra mounts and toys.

Completing the quest for a specialization/weapon unlocks concordance for that specific specialization/weapon. If other specs/weapons also give you extra items, you have to do those specific quests too. You can pick the quests for additional specs up at the council of six in dalaran (does require a certain number of traits in the weapon that goes with that specialization).