On entering the hall, you’re greeted by Ysgramor, a warrior renowned not only for his might but also for creating Nordic writing.  He tells you that three warriors stand ready to aid you in slaying the powerful Alduin- Gormlaith the Fearless, Hakon the Valiant, and Felldir the Old.  This is a heartening prospect, as these three are the very heroes who faced and defeated Alduin in the past- you saw it yourself, after all.  You can find them amongst the other heroes in Sovngarde, or you can wait for them to gather near the right-hand side of the main hall.

It pays a little in lore to wander around first- you can talk to Erlendr the Quick, a friend of Ulfgar’s; Jurgen Windcaller, who founded the Way of the voice; Hunroor the Agile, another companion of Ulfgar; Ulfgar the Unending, who finally made his way home; and Olaf One-Eye, the former King of Skyrim who is responsible not only for Dragonsreach itself, but for trapping Numinex there and keeping him to grant the keep it’s name.

Once you’re in front of the three warriors you seek, Gormlaith enthuses about killing Alduin.  Felldir advises her to slow down and think a moment, though- Alduin’s mist will make things difficult not only by clouding vision but by aiding Alduin in seeking you out as targets.  Fortunately, all four of you can use the Thu’um, so you do have a way to fix this- and if you don’t remember, Felldir will remind you once you get outside.

Heading out of the Hall, you will need to cross the Whalebone Bridge again alongside the three heroes.  Gormlaith is annoyed at the continued mist, but Felldir will advise that with all four of you Shouting the Clear Skies shout, you can break his hold on the valley.  Your shout will prompt the other three heroes, and you will clear maybe a quarter of the valley together- but while your Thu’um recharges, Alduin will respond with a Shout that restores the mist.

Shout again, and the four of you will clear the same area- and Alduin takes slightly longer to restore the mist this time.  Gormlaith despairs that the mist will ever be cleared, but Felldir advises that Alduin is weakening.  The others will Shout without you, so follow their lead from here on.  With only a few more shouts, Alduin will finally stop Shouting the mist back into existence- and instead will Shout a rain of fire into being, indiscriminately pelting the land with meteors of burning death.  This, however, begins the fight with him.  Make sure you have Dragonrend ready, as you cannot hurt him while he is in the air- once you force him to land, though, the three heroes will help you to beat the scales off of him while he belches flame at all of you.  Keep him under the effects of Dragonrend or you won’t accomplish anything by striking at him- but while you can keep him down, you can batter him to his slow death.  Thankfully, other than the constant hail of burning rock and Alduin's impressive health and damage output, this is just like any other dragon fight.