The Phoenix is one of the only tier 4 animals in the game (currently) and is very easy to get to (surprisingly).

Their spawn place is at the very top of the desert temple and can't be bought from anywhere. Phoenixes eat cherry bombs, and they grow on a floating island only accessible by a level 25 pet with the "climb" ability. (The tall black vine). Cherry bombs take a long time to grow, about 14 hours, so leveling up a Phoenix is not something you can do quickly without pet food.