Onyxia's Lair can be cleared in less than 4 minutes these days.
Killing "New" Onyxia Solo
Onyxia has always been fun and profitable so solo. During Wrath she got revamped to level 80, and also started dropping Reins of the Onyxian Drake. Now there are even more reasons to solo her once per week.
On top of the mount, she drops many epics, a quest starting item and a bag that contains epic gems. Some of these gems are still worth lots of wow gold these days, especially when cut, as they are the best gems one can put into level 70 gear.
Also, the epics you're getting here disenchant into up to 2 Abyss Crystals, provided you have the guild perk Bountiful Bags. On most realms, Abyss Crystals continue bringing lots of profit to whoever farms them. Although level 80 epics, and especially weapons, often sell for more than what one Abyss Crystal is worth.
The run takes no more than 3 minutes if you have decent gear.
Tactics? What tactics?
Location: Dustwallow Marsh
If you pull Onyxia to the furthest wall in the room, she has to take a long walk before taking flight. This allows you many more seconds of DPS, which often is enough to nuke her closer to phase 3.
Getting to the instance
Onyxia's Lair is located in the southern part of Dustwallow Marsh. You can see it on the map.
Fastest way to Dustwallow Marsh is by taking the portal to Dalaran in the Panda capital. When in Dalaran, take the portal to Caverns of Time. From here its a short flight over Tanaris and Thousand Needles.
Alternatively, if you are Horde, you can just fly quickly from Orgrimmar.