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Earning the achievement awards the toy  Blazing Wings.

The Firebird's Challenge appears to be a new Darkmoon Faire game.  It likely will involve flying through fiery rings, much like one of the mechanics of the Alysrazor encounter in  Firelands.

The  Blazing Wings were nearly impossible to obtain the first few days of the first  Darkmoon Faire because the fiery rings were sharing between all people on the island and rather than being character-specific as was intended.  Blizzard fixed this first thing the following workday, making the achievement  Brood of Alysrazor finally, well, achievable.

There are about 55 rings available, and you need to get 50 of them in one swoop.  It requires you to be efficient and have a plan, otherwise your flight debuff will wear off and you'll have to try again. 

Here is one possible flight path you can take to earn this achievement and your sweet  Blazing Wings:

Before starting the Firebird's Challenge, make certain that your "Particle Density" is set to at least Fair. You'll otherwise have a difficult time seeing the Blazing Rings.