The Greek hero who completed twelve labors is Heracles, also known as Hercules in Roman mythology. His labors, assigned by King Eurystheus, were penance for murdering his family in a fit of madness induced by Hera. These challenging tasks include slaying the Nemean Lion, capturing the Ceryneian Hind, and obtaining the Golden Apples of the Hesperides. Heracles embodies the archetype of the flawed hero, showcasing themes of strength, determination, and redemption throughout his legendary exploits.