Swift White Hawkstrider

Strangely, this achievement doesn't retroactively give you the Magister's Terrace and Heroic: Magister's Terrace achievements.

Level 85 Mount Solo Farming
This method utilizes speed over kills, but will still reward you with several gold from boss drops and necessary trash kills. All bosses will need to be killed for access to [npc=24664]

First hallway:
Stick to the center and only veer to one side should the 2 pathers approach you. At the end of the hallway, just stick to the center and you will not aggro the last 4 mobs unless there is an Imp pet blocking the way, in which case you need to kill, distract (rogue), or bypass (stealth, [spell=6544], aggro then shadowmeld/vanish, etc.) the mobs.

Opium Den and [npc=24723]
[npc=24723] is linked with the wretched in this room, but not vice-versa. Aggroing him will pull the entire room. So, you have two options: AoE Everything, boss included, or clear the room first, then fight the boss. I would only recommend the first if you have a good health pool, self-healing, and/or good AoE abilities.
5-7 of the wretched are casters that shoot frost and arcane bolts, which you can line-of-sight them to the top platform by kiting the boss to the crystal in the back of the room, while the rest are melee, and will attack you next to the boss. @85, the boss is basically a tank-and-spank melee fight and will periodically run to the closest crystal and absorb it's power, gaining an attack bonus. During the absorption phase, the boss will not be attacking you.

Mana Wrym Hallway
These mobs do an arcane nova effect on death, so killing a large quantity of these mobs without knowing what effect they will have on your health pool is not advised. You can pull 1 or 2 packs at a time with ranged abilities. Periodically, a Blood Elf will enter the hallway carrying an energy cube. He/She will stop in the middle of the hallway, levitate the cube into the air, and all the mana worms will converge on it. This mob has a larger health pool than the mana wyrms and can be used to spread damage over time effects (such as [spell=27243], a Warrior's [spell=84615], or Death Knight Diseases) to all of the mana wyrms.

[npc=24744]
@85 is to use single target abilities on the boss to prevent the [spell=44335] from killing the adds from stacking up too high and killing you. (300 DPS may not sound like much, but it can stack up to 10 times during the fight!) Boss will summon 2 [npc=24745] adds at 85%, 70%, 55%, 40%, and 25% health points. (FYI: If every add was killed during the fight, you would be taking 30,000 arcane damage per second for 30 seconds (equaling 900K damage taken), and have a +500% attack bonus for 30 seconds) This boss can be a bit of a DPS race.

Sunwell Overlook
Make your way into the sunwell overlook where you will find 2 large mechanical. @85, these have a very very short aggro range, and you can simply avoid them by hugging the edges of the hallway. this will lead you to the lower terrace.

Lower Terrace
This essentially becomes a game of Frogger at this point. There is a Blood Elf pather that will go from one end of the room, follow half the circle in the center, go to the other end of the room, then path back using the other side of the circle. Avoid him and stay in the center of the path to avoid the mob packs.
The next room has a large mechanical pather that is easily avoided. You can proceed to Priestess Delrissa's crew straight away as they are not linked with the rest of the room.

[npc=24560]
@85, AoE is the name of the game here. (If you're a Warrior... Stack [spell=12328] with [spell=46924] and win!) Also be sure to have any stun/fear breaking abilities off cool-down, just in case. Focus on the healer classes ([npc=24553]/[npc=24554]) first, if they are up.

Proceed to the final boss room...
You will need to kill the group of 5 mobs here. Await the end of [npc=24664]'s speech, then...

[npc=24664]
@85, He will basically stand there and spam-cast [spell=46164]. Blow any damage increasing cool-downs at the beginning of the fight. You need to beat him down to 50% as quickly as possible to avoid him casting [spell=46165] and [spell=36819]. Ignore the [spell=44194] add.
Once at 50%, he will cast [spell=44224]. Here you want to use any ranged abilities you may have, kiting the large energy orbs away from him, and then sneaking back in for a few swings, but stay just above the ground. Do not land back on the ground unless you want him to throw you back up into the air. If you have a good self-heal ability, you can stay in the orbs for a little bit.
Once downed, the orbs will vanish and you will fall back to the earth (so some possible fall damage here). Small speech, enjoy your loots, and good luck on your mount!

Your experience may very, but it took me 35 attempts on my warrior to get the mount, and the achievement is not awarded until you use the item.

edit: spell links

Heroic only.