There is a guide for Feral Druids to stealth to Anzu and kill him solo. May be you are Feral Druid who take great interest in this guide, let us get down to it without delay.
   First thing first, you should be level 80. For the most part, the gear you need to do this requires it.
Then you must be reasonably well-geared and must have done the Epic Flight Form Quest. None of that silly, "I waited until 71 and just bought it from the trainer" stuff, you have to be one of the druids who earned epic flight form.
At a pinch, you can bring a potion or a healthstone, or both. Probably you won't need him, but there is a chance that you can be stunned at the beginning of a banish phase, in which case, you'll want the extra healing.
With that out of the way, head to Sethekk Halls! In case you've forgotten, it's in Auchindoun. It's the east instance. When you enter the instance, hit cat form and stealth.
It is important to note what mobs are in what pull when you clear the trash for each pull. As the illustration below suggests, there is a specific order in which you want to do things.
At the beginning of each trash pull pop Berserk and Barkskin. Berserk will keep you from being feared, and Barkskin should be used every cool-down anyway. Target a Prophet, spam Mangle and Maul until it dies. If there's another Prophet, do the same.
The drake that pats in a circle around Anzu's summoning claw, the first thing you want to do is buff Thorns and Mark of the Wild and then pull the group on the southeast corner. Heal up using Regrowth followed by Nourish spam. Pull the drake circling the middle when he's closest to you. Then pull the remaining groups in any order, waiting for your Berserk in between each pull. It's not necessary to do but Berserk makes these pulls a lot easier both by increasing DPS substantially and removing the possibility for fear.
If you wait near the coffer, he won't pull right away. When you're ready pull him. Start off by using the Eagle Spirit macro. This will not pull Anzu, so hit Bear Form, Enrage, and pull him over to the tanking spot, making sure to position him in a way that is outside of line of sight to the healing spot. When he is positioned, pop Berserk and spam Mangle + Maul. When that expires, start using Lacerate +Mangle + Maul, refreshing Demoralizing Roar and Faerie Fire when needed. Keep 5 stacks of Lacerate up. On occasion, Anzu will stun you but this should not be a problem at this point.
Eventually, he will banish himself, at which point you should run to the healing spot. Cast Regrowth on yourself, and then spam Nourish until you are either at full health or half mana. Use your Eagle Spirit macro and go back into bear, Demoralizing Shout the birds, and use Swipe + Maul to get the birds down. With nameplates up, you can easily target the lowest health bird to make sure it dies first, then move to the next lowest, and so on.
When Anzu comes back in the fight, you may still have one or two birds up. Get them down quickly, reposition Anzu and get back to fighting him the way you were before, using Lacerate + Mangle +Maul and refreshing Demoralizing Roar and Faerie Fire when needed. If berserk gets off cool-down, saves it. You may find yourself getting pretty low during this phase. If that happens, use Survival Instincts +Frenzied Regeneration. Don't use Maul while regenerating. Continue through this phase until he banishes himself again.
When he does, it's back to the healing spot. Again, cast Regrowth on yourself; spam Nourish until you are either at full health or half mana. Half mana is much more likely at this point, unless you just did regeneration. If he stuns you at the beginning, you only have time for a Re-growth + Nourish. You have to use a potion or a healthstone and berserk on the birds to clear then quickly, Anzu should come back out. At this point, there is no Banish phase so you can tank him anywhere. Just keep up your rotation of Lacerate +Mangle +Maul, keep Demoralizing Roar and Faerie Fire up, and you should be done! When he falls, pray to the loot gods for your mount!
Keeping Anzu out of line of sight while you are healing is the most important thing. If he sees you cast a spell, he will put Spell Bomb, which drains 2000 mana and does 100 damages on you whenever you cast a spell. Since that's likely a third of your mana pool, you can't afford to get hit by it even once.