The hero known for battling monsters and demonstrating cunning in mythology is Odysseus from Greek myth. Renowned for his cleverness and resourcefulness, he faced various challenges during his journey home from the Trojan War, including encounters with formidable creatures such as the Cyclops and Scylla. Odysseus' adventures illustrate themes of intelligence over brute strength, showcasing how wit and strategy can prevail in overcoming life's obstacles, making him a quintessential figure in mythological storytelling.