Achelous was born to Oceanus, the Titan whose vast waters encircle the world, and Tethys, the Titaness who bore three thousand river gods and three thousand Oceanid nymphs. Some say his mother was Gaia, the primordial Earth herself. From his birth in the swirling depths, Achelous was destined for greatness. He was named "silver-swirling Achelous" among the mightiest of the river gods, and called the prince of all rivers. Only Zeus, the king of the gods, surpassed him in strength, though among all rivers Achelous stood without peer. The river that bore his name rose in the Pindus mountain range and flowed for more than two hundred kilometres through the heart of Aetolia and Acarnania, forming the disputed boundary between those lands before emptying into the Ionian Sea. Its roaring waters sounded like the voice of a bull, and its winding course through gorges and channels suggested the coils of a serpent. The Greeks saw the god in the river, and the river in the god.

The most famous tale of Achelous is his contest with Heracles for the hand of Deianira, the beautiful princess of Calydon and daughter of King Oeneus. Achelous had courted her long, pressing his suit with the authority of a god who ruled the very waters that nourished her father's kingdom. But Heracles, the son of Zeus and the mortal woman Alcmene, arrived in Calydon and claimed Deianira for himself. Rather than let words decide the matter, Heracles challenged the river god to a wrestling match. They met before the court, and Achelous fought first in his human form, a powerful man with water dripping from his hair and beard, locking arms with the hero in the classical stance. Heracles threw him to the ground. Achelous then transformed into a serpent, sheeny and coiled, slipping from the hero's grip with the sinuous ease of his own river. Heracles laughed, for he had strangled serpents in his cradle as an infant. Finally Achelous became a furious bull, lowering his broad head and charging with horns that could tear the earth itself. Heracles seized those horns as handles, flipped the beast to the ground, and with a mighty jerk snapped off one of them. The river god retreated in pain and humiliation beneath his waters, and Heracles carried Deianira away as his bride.

In another tale, told in the pages of the Metamorphoses, Achelous showed a gentler face. The hero Theseus was travelling home from the great boar hunt at Calydon when a flood barred his way. Achelous rose from his swollen stream and invited the mortal into his watery abode, a palace of spongy pumice with a moss floor and a roof of oyster shells, where barefoot nymphs served wine in jewelled cups. As they dined, Theseus pointed to islands scattered across the water and asked their names. Achelous told him they were the Echinades, once nymphs who had forgotten to invite him to their festival. In his fury the river god had swelled to flood, tearing forest and field away and sweeping the nymphs into the sea, where his waters and the ocean split the land into islands. Then Achelous pointed to a distant isle called Perimele, and confessed that she had been a maiden he loved, thrown from a cliff by her father when he discovered their union. Achelous had caught her and begged Poseidon, god of the sea, to transform her into land, and the god granted his prayer. Even a defeated god, it seemed, could love and grieve.

Achelous was father to many children besides the waters he spawned. By Melpomene, one of the nine Muses who presided over the arts and goddess of tragedy, he fathered the Sirens, the bird-bodied women whose song was so beautiful that sailors steered toward their island and died on the rocks. By other nymphs and mortal women he fathered nymphs of his own, including Callirhoe, whom he gave in marriage to Alcmaeon, one of the Epigoni, the sons of the Seven Champions who had fallen against Thebes. The river god also purified Alcmaeon when the Erinyes, the avenging spirits of blood-guilt, pursued him for killing his treacherous mother. In every tale, Achelous stands at the centre of the boundary between the wild and the civilised, the divine and the mortal, offering both destruction and sanctuary.

The broken horn of Achelous became one of the most enduring symbols in Western culture. The Naiads, the freshwater nymphs who attended him, took the severed horn and filled it with fruits and flowers, consecrating it as the Cornucopia, the Horn of Plenty. Some say Achelous later traded the horn of Amalthea, the goat who nursed infant Zeus, to recover his own. Either way, the image of the overflowing horn passed into the hands of gods of abundance and eventually onto Roman coins, Renaissance paintings, and the state seals of modern America. Achelous himself was worshipped throughout Greece as the representative of fresh water itself. The oracle at Dodona, the oldest sanctuary of Zeus, regularly commanded supplicants to offer sacrifice to Achelous before any other god, and his name was invoked in oaths and prayers from Athens to Sicily. On coins of Acarnania he was shown as a bull with the face of an old man, crowned with a single horn. His image appeared on the throne of Apollo at Amyklai near Sparta and in a statue of cedar and gold at Olympia. The river still bears his name today, flowing through the rainiest part of Greece, a quiet stream where once a god roared.