Phoenix (or Adar Flam, the name given to it by fans) is one of several unused colossi that did not make it into the final version of Shadow of the Colossus.
The guidebook gives information on how Phoenix had to be defeated: "Its body was wreathed in flame. You defeated it by plunging it into a lake". This indicates that Wander was not able to climb its body straight away. In all released screenshots of Phoenix, Wander is seen riding Agro, so it can be assumed she was vital to this battle.
According to an old Team Ico Gamers Blog post, Phoenix was removed for being overpowered and also because it required a huge arena due to its attacks. 
Another screenshot of Phoenix.
Wander and Agro near Phoenix. Note its long, ostrich-like neck.
Another image of Phoenix in which it appears to be glowing. The source of this image is unknown.