Step 1:
*You have to take all of your gear off, it will make your Serpent Sting crit, messing up this guide.
*Shoot them with a Serpent Sting (Immediatly click away after this, or you will shoot him with your Auto attack.)
If you are having trouble clicking away in time, I have prepared this macro for you:
/use Serpent Sting
/target yourownname
Step 2:
*Cast Tame Beast at the exact moment, the Serpent Sting does its first amount of damage.
If the Pet dies, you cast tame too late.
If you get a brown hawk, you cast tame too early.
Do not expect to do it right the first time, and keep making small adjustments.
Step 3:
*If you do it just right, the target will Die and be Tamed at the same time.
*You now have to use Revive Pet instantly after it was tamed, to make the corpse vanish. (When I say instantly, I mean INSTANTLY)
*Now you cancel the revive, after the corpse is gone.
You will not see a Portrait of the beast in your Call Pet button, but it is there alright.
Step 4:
*You relog.
*Now Select the pet slot you tamed your Oiled Hawk in. ("Your pet is dead.")
*So now you revive him and enjoy your new insanely rare pet!