This is not really a step by step guide, as a great deal of luck is involved (misses, crits, swaps, etc), but it might be useful to people who are struggling with the fight (so were I). The reward is a spectral bunny, which you can see at the end. I swapped team setup, so if you're not interested in all my fails with the first team (and a couple with the second) then click towards the end where I finally killed it.
I hope this can be of any use to somebody:
https://www.facebook.com/plugins/vid...xt=0&width=560
Good luck on your fight.It's not easy. The reward is super cute, though. I like it how they make you do something, instead of just mailing you another pet.
The algalon fight was considerably harder than the celestial tournament in mists of pandaria.