As a former archer I have always had a soft spot for tales, legends and myths that involve bow, arrows, and infinite badassery. With the sudden popularity of archery due to movies and books, I believe it is time to take a good spotting look at the contestants.
Katniss (The Hunger Games), Merida (Brave), Susan Pevensie (Chronicles of Narnia), Hanna (Hanna), Neytiri (Avatar)
Artemis/Diana - Goddess of the Hunt
The Amazons - Even though not all Amazons used bow and arrow as a main weapon, they were rumored to have cut off one breast to make archery easier. As a femare archer, I don't really see a point in this, but thus goes the story.
Nymphai Hyperboreai - Nymphs, followers of Artemis, responsible for skills in archery
Camilla and Opis - Huntresses of Roman legends
Atalanta - the ultimate tomboy of Greek mythology
Skadi - goddess of archery, formerly a frost giant
Satet - archer goddess of Egypt
Legolas (Lord of the Rings), Hawkeye (Avengers), Green Arrow (Justice League), Robin Hood (countless movies of Robin Hood), Prince Willian (Snow White and the Huntsman) etc. etc. etc.
Apollo - Greek god of the Sun, music, art, archery, and ridiculously photogenic (sculpture-genic?...) people
Kheiron - The Centaur, mentor to countless Greek heroes. Seen as an archer in the constellation Saggitarius.
Eros - better known as Cupid
Odysseus - there is that one famous bit about the bow that no one was strong enough to string...
Philoctetes - legendary Greek archer in the Trojan war
Paris - Dumb as he was, he did hit a guy in the ankle from the walls of Troy...
Ullr - Norse god of archery and hunting
Egil - Legendary archer of Norse mythology (way before William Tell)
William Tell - National folk hero of Switzerland. Apple, boy, arrows, you know the drill.
Yi, the Archer - Legendary person in Chinese mythology. Shot the Sun off the sky. Nine times.
Attila the Hun - Not usually famous for this archery skills, but according to Hungarian folk legend he was quite spectacularly good at it anyway
Robin Hood - I don't have to introduce this guy
Ekalavya - Legendary archer from the Indian epic Mahabharata. Self-trained, left-handed, has nine fingers. What's your excuse?
(By the way, read the Mahabharata for a whole lineup of ridiculously talented archers)
Kamadeva - the Hindu version of Cupid. With more flowers.
Erekhe Mergen - Legendary Mongolian archer, shot a few suns off the sky for good measure, no biggie
Now the only remaining question is:
Who would win?...