Warning: This is a very geeky WoW post. If you are not struggling with the cloak phase of the legendary questline, you may want to skip this for something of more general interest.
Most people I know are doing the legendary questline with one or more characters. After the solo scenario in the forge, to get the legendary metagem, I seriously questioned the wisdom of carrying on with my alts, but I'm determined to do the whole thing with my hunter. I cleared the Celestial Blessings hurdle and got my cloak after only about 8 tries on Saturday night, but the ranged DPS fight not hunter-friendly at all. I was thinking I had to be the last hunter on my server to get the cloak, but as I was leaving the temple, another hunter whispered me -- did you beat it? what did you do?
I'm no hunter guru, but here's what worked for me.
First, people have claimed each of the specs is 'the best' for this fight, and that each of the other specs is 'impossible' so obviously any of them will work. I would suggest either Marks or Survival just because those give you the ability to do damage even if your pet is down, or on another target, but if you're a die-hard Beastmaster, then go for it. I am assuming that you're sufficiently geared up, having run Throne of Thunder for umpteen weeks collecting those Titan Runestones. I don't have the time to raid regularly, so I went into this with mostly LFR gear, and an ilevel of 514. Hardly awesome, but certainly good enough.
You will need to adjust your talents and glyphs from your usual raiding configuration. This is what I went with; other choices may also be completely viable (Barrage for more AoE, for example, though I found the slow from Glaive Toss helped more). If you don't complete the scenario on the first try, think about what went wrong and whether tweaking these suggestions would help you. Note that my choices are focused around movement -- either speeding me up, or slowing the adds down.
Posthaste: the movement speed boost will help you kite the Neltharion's Tears. Glyph Liberation for the heals. Remember to use Disengage liberally during the fight.
Binding Shot and Glaive Toss will help slow the Tears.
Spirit Bond + Glyph of Animal Bond = improved self-healing. You will need it. I would go so far as to say that these choices are essential, but feel free to prove me wrong on that.
Thrill of the Hunt means a lot of free Multishots, which is good when you're trying to burn down the Tears.
AMoC and your other dots (Serpent Sting, Black Arrow, etc) go on Wrathion. Try to keep them up as much as possible during the adds phases.
I went with my Marksmanship spec for this, so I used Glyph of Aimed Shot, so I could cast it on the move. In retrospect, glyphing Chimera Shot would also have been a good choice. If you're using a different spec, pick whatever glyph makes most sense, remembering that mobility is key here. I didn't tweak my minor glyphs, since they have not-very-much impact on abilities.
For my pet, I used a turtle specced Ferocity with Shell Shield and Cower on autocast. I had to use Heart of the Phoenix once, but otherwise the turtle stayed alive. Whatever pet you use, I do suggest speccing it to Ferocity for the extra damage, and try to keep it on Wrathion.
After you ring the gong, the encounter doesn't start until you hit Wrathion, so get yourself together. Flask up, eat Sea Mist Rice Noodles. Get behind him, pre-pot, and blow your cooldowns. Stay behind him as best you can to avoid his frontal cone attack and to take advantage of the damage buff.
When he summons the Tears, kite them and kill them, using everything you've got to slow them. Drop Freezing Trap, use Binding Shot, Glaive Toss and Multishot, Disengage when necessary. The Tears die pretty easily, but they hurt if they get near you and they gain movement speed as long as they're up, so nuke them as fast as you can.
Keep up as much damage on Wrathion as you can while you kite adds -- dots, pet, traps -- but focus on getting the adds down before they kill you. All the strats that suggest running up on the balcony and using Feign Death don't work anymore, so don't try that. The adds will just run up to you and kill you.
You should run up to the balcony when Wrathion casts his Mirror Images. Don't try to blow them up. Just run for the back of the balcony. Stand behind Yu'lon. If the Tears follow you up there, kite them around the back of the balcony and kill them, but don't run back downstairs until the Mirror Image phase is over. You will know it is over because Wrathion will come running up to the balcony looking to kill you. He will warp back downstairs for the next mirror phase, so don't worry about that.
If there are no Tears chasing you, Mirror phase is also a good time to rez your pet and bandage yourself if you need to.
And that's really it. Kite and kill the Tears, sic your pet and your dots on that overgrown lizard prince, and avoid the damage as much as possible. Do not feel bad if it takes you a few tries, or more than a few tries. It is not meant to be easy. That thing Yu'lon says about how wisdom is knowing when to do nothing is good advice.
Next stop, the Timeless Isle for the quest to upgrade the cloak.