- Read the Elder Scroll at the Throat of the World
- Learn how to use the 'Dragonrend' shout
- Defeat Alduin
Upon arriving back at the Throat of the World, Paarthurnax will tell you he sees something different in you, that you must have the Elder Scroll now. He'll then tell you to go to the Time Wound and read The Elder Scroll.
Upon viewing the Elder Scroll, you will see a vision of the past, where the prior heroes who defeated Alduin stand ready for Alduin to attack. When he does, they will use the Dragonrend shout, teaching the shout to you in the process. Watch them fight Alduin in their time.
Directly after the cutscene, when you arrive back in the present, Alduin will appear at the Throat of the World. Paarthurnax and Alduin will take flight, attacking each other in the air. When the chance arises, use Dragonrend on Alduin, forcing him to the ground. It can be rather difficult distinguishing between the two dragons if the battle is done at night or while it is snowing. Inadvertently using Dragonrend on Paarthurnax and therefore grounding him often makes Alduin hover in one place in the air while attacking Paarthurnax, thus making it easier to strike him with Dragonrend, although it is better to ground Alduin alone. The quest arrow on your compass always points to Alduin, so use that to distinguish the two.
When Alduin is grounded, you must attack him as much as you can before he takes flight again (Marked for Death is pretty helpful). This may take a few tries, since he has a huge health pool and does reasonable damage. Be wary of Alduin's "Dragon Storm Call" shout, which causes fiery meteors to rain from the sky. These cause both fire and physical damage. Using Dragonrend immediately when it recharges will keep Alduin grounded for the whole fight. When Alduin's health drops to zero, he tells you he underestimated you, but no one can defeat him, not even Dovahkiin. He will then fly off, completing the quest.
