Rama

"Preserver's marksmanship is one of his many unequalled qualities."

- Lore

Ramachandra, widely known as Rama is the main protagonist of Ramayana. He is the crown prince of the Kosala Kingdom, the son of King Dasharatha of the Solar Dynasty and Queen Kausalya. He also happens to be the seventh incarnation of the God Vishnu, born on Earth for the sole purpose of slaying the wicked Ravana.

Indian Mythology
The epic begins in the city of Ayodhya whose king, Dasaratha, is in despair since he has no children to inherit his kingdom. He performs a great fire sacrifice and his three wives, in consequence, bear four sons: Rama, Bharata, and twins Lakshmana and Shatrughna. When Rama, his eldest and favorite son, turns sixteen, the sage Vishwamitra requests his help in taking down the demons. In other news, the neighboring King Janaka despairs that nobody can complete the Engagement Challenge to win the hand of his beautiful daughter Sita, as many suitors have tried and failed to even lift the bow of Shiva (which he ordered must be strung). Rama, naturally, breaks the bow, and marriages are arranged left and right between the two kingdoms. Rama and Sita reside together in peace for about a decade.

Dasaratha, having grown old, is about to hand over his position to Rama, however his youngest and favorite wife Kaikeyi convinces him to fulfill The Promise he had made years ago. She then asks that Rama be exiled for fourteen years and her son, Bharata, be crowned. Dasaratha reluctantly does so, but he dies of heartbreak not long after. Lakshmana tags along with Rama and Sita, leaving his own wife and twin brother behind in Ayodhya. Meanwhile, Bharata finds Rama in the forest and declares that the throne rightfully belongs to the latter. When Rama refuses, Bharata accepts, but threatens to kill himself if Rama doesn't promptly return when his exile ends.

Rama, Lakshmana, and Sita eventually settle into a life of exile. Surpanakha, a sister of the demon king Ravana, is entranced by the brothers' good looks and tries to seduce them. Ever faithful, Rama and Lakshmana deny her advances, and the latter cuts off her nose. Naturally, when Ravana hears of this, he's pissed off and orders the shape-shifting demon Maricha to turn into a golden deer. Sita is entranced by the deer, and asks Rama to capture it for her. He reluctantly leaves her under Lakshmana's guard, but when Sita thinks she hears him cry for help, she convinces Lakshmana to go after him. Of course, it was all a distraction, as Ravana kidnaps Sita and brings her to the island city of Lanka, separated from the mainland by a giant ocean, where he tries to force her to marry him.

The rest of the epic describes the rescue Rama embarks upon with Hanuman — greatest of the monkey heroes, trickster archetype, and son of a wind god — who helps him search for Sita when Sugriva, his leader, is returned to the throne of Kishkinda. Hanuman meets Sita clandestinely in Lanka and asks her to return home with him, but she denies his request, saying that Rama should be the one to rescue her. He is captured by Ravana's forces, but Ravana's righteous brother Vibheeshana convinces Ravana not to kill him and instead only burn his tail. Hanuman then torches the entire city.

What follows is Rama and company attacking Lanka by building a giant bridge. A lengthy battle then happens, in which Ravana is defeated. Sita is returned to Rama, but he doubts her chastity. She then goes through the Agni Parishka, where she steps into a fire to prove that she did not sleep with Ravana. The flames do not burn her, she is declared innocent, and the party returns to Ayodhya where they rule peacefully.

Hades
Though Rama himself doesn't physically appear in the game, his legendary weapon the Coronacht is seen and can be used by Zagreus, implying that he may not have been born yet, or that he died some time before.

Additional notes
For additional information on Rama that does not pertain to Hades, see Wikipedia's article: Rama