Morrid and Moomuerto on the official WoW forums claim to have soloed Anzu as a moonkin!
Hearing of these success's has inspired me to keep trying (yes I've been failing at this, although I've found a proper feral tank spec with average gear quite easy)
Morrid's stats are quite decent compared to the average chicken.
2753 spell power
He says he feels it is really important to keep the eagle totem up (the one that reduces dmg by 500)
Moomuerto has posted a short guide which I will copy here, since we know how the WoW forums like to eat posts
Moomuerto feels it's not necessary to use the totems.
Here's the way to do the fight as moonkin, although it might take some practice to get down.
1.) If you enter the room, the wall on the left is one i engaged him from. Stand as close to the wall as you can.
2.)throw a regrowth on the eagle and...hawk i think (not needed but helps) and then regrowth, rejuv yourself, moonkin form and charge up a starfire on him, dot him up and barkskin once he gets in melee range, he never put the curse on me in this first phase so just nuke him down with barkskin on until he shifts into his ghosty form.
3.) as soon as he shifts start running to the opposite wall of the room and hot yourself to full, shouldn't need much, be mindful of the curse while running as this is when he starts using it. Get ready for the birds.
4.) He will generally cast his long 5 second stun on you while youre at the opposite wall, wait for the stun before you hurricane the birds down. Also, dont hurricane the birds down until you see your barkskin will be off cooldown in around 10 seconds or so. Anzu will charge you as soon as they die.
5.) once the birds are dead, he will start running towards you from the opposite wall (where you first pulled him) now is the time to regrowth, rejuv, lifebloom yourself before he reaches you. make sure you are not casting if he puts the curse on you, cancel your cast and decurse yourself. 6.) now your barkskin should be up again so you should be able to nuke him with full hots on yourself. use treants / starfall / innervate if needed. The only thing different about this time is that he will randomly put the curse on you while you're casting wrath / starfire....its very important to be ready to cancel cast and decurse yourself because you will take too much damage otherwise. Nuke him down to a certain % and he will ghost form again... 7
.) repeat steps 3-6, kill and loot. Equipping a pvp trinket helps a lot for his 5 sec stun, especially when first learning how to solo this as a moonkin. I used mostly 226-232-245 pve gear.
The biggest challenge I've found when doing this is making sure you get the de-curse off in time, unfortunately I do get cursed during the first stage of the fight, and sometimes he puts it on you just before your cast gets off, also I'm probably getting old and losing a bit of reaction time, but i will endeavor.