The fight begins with a physical clash in Horus’s Throne Room. The infinite expanse of darkness that made his throne recedes giving way to a physical space, as Horus focuses his power to face his father instead. Their first clash "shakes the world", meaning the infinite dimension in the Warp that Horus has turned his throne room into, and shatters the darkness.They clash with such speed and power that the onlookers can’t perceive or hear the fight, and if they even step close to their duel they will be annihilated, the concentration of power around them being like walking into the core of a dying star. There is no sound to the battle, just a constant staccato white noise, because they are hitting each other so hard that the sound of one clash is engulfed by the next, and on and on.The Emperor strikes with the power of a blazing supernova, but Horus is mightier, he has the power of a Black Hole that devours all light, and he is winning. He is fueled by the infinite power of Chaos, while The Emperor's own power is finite.
But of course, Horus and The Emperor aren’t just clashing physically, their battle is psychic and spiritual, happening in the Warp, taking place not just across the three spatial dimensions of Realspace, but across the infinite dimensions and planes of the Empyrean. The Emperor strikes Horus along the eighteenth angle of non-space, and Horus diverts a blow to the sixty-sixth oblique direction, then dodges a killing blow by sidestepping into an adjacent reality. Their fight cannot be perceived by mortal senses, the previously described fight is just the slightest sliver of what is actually going on.
Eventually, The Emperor starts to take advantage of the fact that in Horus’s realm of Chaos, all of time and space has collapsed into a single isochronal instant, a realm where direction and duration has no meaning, and so he takes the fight beyond just the current time and place, to instead fight Horus across everywhere and EVERYWHEN.
Suddenly, Horus and the Emperor are on the planet Cthonia, on the day of Horus’s finding. This isn’t a projection or a memory, they are literally in Cthonia. Then they are in the Himalayan mountains before Imperial Times, then in Ultramar during the Horus Heresy, on Ullanor during the Great Crusade, on Moloch when The Emperor made his deal with the Chaps Gods, on ancient Terra during World War I, on on Ancient Greece, or in Prehistoric Times, and more and more all across the galaxy.All of these duels are happening simultaneously, with Horus killing the Emperor along several battlefronts, and the Emperor winning others. Each battle is just an aspect of the Greater Duel, for either force to win, their opponent has to be killed on all battlefronts.
The fight then escalates again, with The Emperor takes the fight to the symbolic and archetypal level, summoning his Deck of Tarot cards, casting each card to summons aspects of himself and of humanity. The Angel, The Pilgrim, The Final Wall, The Throne, etc etc. Horus responds by summoning his own Tarot Deck, built out of Chaos. He summons The Daemon, The Lunar Wolf, The Spectre, The Lightning Tower, The Shattered World. These aspects clash across metaphysical planes of the Warp, engaging in symbolic combat.
In one plane, Horus and The Emperor are wolves hunting each other in the forest, in another they are ancient Hellenic warriors with bronze shields and spears, in another they are planets and suns clashing in the void, in another they are a Hawk and a Serpent, in one The Emperor is a Knight fighting a Dragon, in another they are gunslingers facing off in a desert, in one they are naked cavemen killing each other with rocks.Horus's Deck is stronger. The Emperor's deck represents aspects of Himself, His Sons, and Humanity, while Horus's cards are embodiments of Chaos, which is Infinite and omnipresent and primordial. One by one, The Emperor's aspects begin to be destroyed, until he only has a handful of cards left.
Standing victorious, Horus starts to beat The Emperor down, torturing and maiming him sadistically, slicing his throat, breaking his bones, cracking his ribs hard enough to puncture his lung, gouging his left eye out, smashing his skull, etc etc. He leaves him broken on the brink of death, at which point he extends a hand, offering to heal The Emperor so long as he accepts a place at his side.
At this point, the onlookers actually attack Horus. The Emperor's last remaining Custodian charges at Horus but is smacked aside, same for the Loken, the Space Marine. John Grammaticus uses a Word of Power to halt Horus in place for a few seconds so he can be pushed away from The Emperor, but this too is futile. Finally, Ollanius Perrson stands between The Emperor and Horus with nothing but a lasrifle, shooting Horus until he too is evaporated by his talon.
Meanwhile on Terra, Euphrati Keeler has 2 million pilgrims praying for The Emperor at the Astronomicon, and their faith is enough to relight the psychic fire of the beacon. All 2 million pilgrims are immolated, and their faith and their soul is sent towards The Emperor. The Emperor channels the power of their souls and their faith into a focused psychic beam that hits Horus as his guard is down, pushing the influence of Chaos away from Horus for a brief moment. Horus, now himself again, begs for The Emperor to kill him. Half-dead and mutilated, The Emperor lunges forward and stabs his heart with the Athame Dagger, channeling all of his remaining power into it, obliterating Horus’s soul forever.
Horus’s death sends a psychic shockwave through Realspace and The Warp, shattering and breaking the various different planes of unreality that they were previously fighting on across the Warp, and making stars across the rim of the galaxy spontaneously explode in supernovas.
Then The Emperor faints and collapses on top of his son's corpse.