The idea is to shock-and-awe your opponent. Don't ever let them do damage to you early on; Remove, remove, remove! Make sure you use Wasteland Viper as a defender when appropriate. And also, make sure you sacrifice Centaur's Herald when appropriate. Play the early game (first 1-5 turns) smart and relentlessly, and you will be rewarded with very tough creatures for a low cost, and your opponent will be very crippled.
Keep your opponent crippled middle and late game with Slum Reaper (Sacrifice him if you must), Vraska the Unseen, Gaze of Granite, Hero's Downfall, and whatever else you may get; REMOVE!
Mid game, you should be able to have a strong Nighthowler, Nemesis of Mortals (or both), or Desecration Demon, on the battlefield. Your opponent should have very little to do about this.
Clench the game one of two ways:
Korozda Guildmage: Use this creatures ability to give a tough Nighthowler, or a monstrous Nemesis of Mortals, 1+1 and intimidate till end of turn.
Jarad, Golgari Lich Lord: Use this creature's ability to sacrifice a Nemesis, or tough Nighthowler. Make sure you attack first if appropriate to do so.
The biggest enemy of this deck is a well constructed blue or black control deck. Mono Black in particular could also prove to be a dangerous foe. Sideboard in creatures with protection from blue or Dark Betrayal as needed. Hopefully these will be enough. Don't forget, you still have options. Some removal, like Abrupt Decay and Vraska the Unseen are perfect to get rid of annoying things like Detention Sphere, Chained to the Rocks, etc.
Story behind Phoenix Corpse :
Long ago, the phoenix used to keep watch over mankind from the skies. It has been said that they exist to track of human progress, help guide them to a higher state of being.
A thousand years passed, and not a single Phoenix has been seen for centuries. It is said that once the Phoenix disappeared, mankind quickly started to devour their surroundings. They started to breed more, cut down forests, and build toxic factories in order to support the war efforts against the Elf's.
The Forest has always belonged to the Elf's, just as the Humans have controlled the Plains and coast lines. When the humans invaded the Forests, the Elf's responded against the aggression to protect their home. It is said that the Humans and Elf's are brothers and sisters from the same parents, but once the Phoenix left, the spirit of comradery and peace left the earth with them, and the two formed different factions.
One pocket of forest in particular remains elusive from the war. No one that has ever stumbled upon it has lived to tell about it. Small, vicious snakes with the ability to kill an intruder in a single blow roam it's edges; along with lethal booby traps. Elf scouts also have an established perimeter set up there.
Even if someone does make it in, they aren't likely to last very long. Giant snakes inhabit the forest in the areas uninhabited by Elf's. There is speculation that this is the forest where all the Phoenix went to die together. Aside from giant snakes, it is also said that giant, horrifying looking creatures lurk the forest. One look into their eyes, and they will reap your soul from your body. Legend has it, the Forest took their bodies in exchange for freeing their souls. However, some suspect the Forest of being under the control of pure evil; Using the bodies of those who perished in it, and caputring souls. The Efl's who inhabit the Forest seem to have little control over the Forest, but seem to have some sort of protection from it.