Who discovered anatomy?
Anatomy wasn't a discovery itself, so no one discovered, but it was a series of discoveries under one scientific discipline, from the Egyptians through the Greeks and into modern Europe.
No one really "discovered" anatomy like people discovered the pentaquark or Australia, it was more of a gradual process of different discoveries within the science of anatomy.
Anatomy began roughly with the ancient Egyptians, who were actually very advanced scientifically for their era. Mummification was a great opportunity to examine the insides of bodies, and it was even the Egyptians who discovered the left hemisphere of the brain controlled the right half of the body and vice versa.
The Edwin Smith Surgical Papyrus was a document written around 1600BC, which shows various organs of the body such as the heart, liver and even hypothalamus. However, it is far from perfect, describing the heart as not just the center of blood circulation, but urine, tears and semen as well.
It was then the Greeks who developed the technique and terminology, much of which is still drawn upon today. Aristotle and his contemporaries developed an empirically (observationally) based system of animal dissections, and from there anatomy evolved through Europe, through Galen and da Vinci, the anatomist-artist among copious other titles, into Gray's Anatomy, the first and most major English-language textbook on anatomy. Nowadays most breakthroughs are cytological or histological and many can't be seen with the naked eye.