So you know about the lore:
Akatosh, Dragon God of Time
The Avatar of Akatosh as seen in OblivionAkatosh (Auri-El to the Aldmer and Alduin to the Nords) is the chief deity of the Nine Divines (the prescribed religious cults of Cyrodiil and its provinces), and one of two deities found in every Tamrielic religion (the other is Lorkhan), save only the Dunmeri Tribunal of self-made gods. His avatar is a dragon, and he is often called the Dragon God of Time. He is generally considered to be the first of the Gods to form in the Beginning Place; after his establishment, other spirits found the process of being easier and the various pantheons of the world emerged. The Aedra is the ultimate God of the Cyrodiilic Empire, where he embodies the qualities of endurance, invincibility, and everlasting legitimacy while promoting the virtues of duty, service, and obedience. He is the patron of The Akatosh Chantry, the religious order devoted to the worship and glorification of him, who refer to him as the "Great Dragon". He is thought to have played a benevolent role in the Warp in the West.
Akatosh
Most traces of Akatosh disappeared from ancient Chimer legends during their so-called 'exodus', primarily due to that god's association and esteem with the Altmeri. However, several aspects of Akatosh which seem important to the mortal races, namely immortality, historicity, and genealogy, have conveniently resurfaced in Almalexia, the most popular of Morrowind's divine Tribunal; as a mother-figure, she also embodies the idea of being a progenitor (albeit a female rather than male one). So one could say that, at least, the qualities of Akatosh are not entirely neglected among the Dunmer, even if his name is.
Akatosh was involved in the forging of the Covenant with the new Empire of humanity, and his blood was mystically joined with Alessia and her heirs. The Amulet of Kings was the primary token of this patronage, and it allowed the new Empire of Cyrodiil to benefit from the stabilizing influence of White Gold Tower, maintaining the barrier between Mundus and the Planes of Oblivion. When that barrier was threatened during the Oblivion Crisis, Martin Septim was able to summon Akatosh's spirit and transform himself into the avatar of Akatosh, which appeared in the shape of a giant dragon made of fire. This avatar dragon defeated Mehrunes Dagon, reestablishing the mystical barrier between Tamriel and the Daedric Realms. The avatar transformed into a statue, now located inside the ruined Temple of the One.
Akatosh is accredited with creating Auriel's Shield and Auriel's Bow.
Alduin
Alduin is the Nordic variation of Akatosh, and only superficially resembles his counterpart in the Eight Divines. For example, Alduin's sobriquet, 'the world eater', comes from myths that depict him as the horrible, rauaging firestorm that destroyed the last world to begin this one. Nords therefore see the god of time as both creator and harbinger of the apocalypse. He is not the chief of the Nordic pantheon (in fact, that pantheon has no chief; see Shor) but its wellspring, albeit a grim and frightening one.
Another legend says that Alduin can "eat" away the age of his victims, and that he once ate the entire Nord population down to age six after being summoned by Orkey.
Alkosh, Dragon King of Cats
Pre-ri'Datta Dynasty Anaquinine deity. Variation on the Altmeri Auri-El, and thus an Akatosh-as-culture-hero for the earliest Khajiiti. His worship was co-opted during the establishment of the Riddle'Thar, and he still enjoys immense popularity in Elsweyr's wasteland regions. He is depicted as a fearsome dragon, a creature the Khajiiti say 'is just a real big cat'. Repelled an early Aldmeri pogrom of Pelinal Whitestrake during mythic times.
How to defeat him?Perhaps with Aluriel's Bow? Its made from his magic, it makes sense that his own magic would harm him.
Maybe you cant, if he is invincible... maybe proving your devotion to duty and virtue you will be deemed worthy and Akatosh/Alduin will agree to leave the world be and grant you the Amulet of Kings?
Maybe in his avataar form you can defeat him. Its not a full god form so perhaps in physical form he is vulnerable and not all powerful?
Or maybe we can appease him with a sacrifice?