New main objective: Help the heroes of Sovngarde dispel Alduin's mist
Follow the heroes of Sovngarde, leaving the Hall of Valor. Cross the bridge previously guarded by Tsun. Stop after reaching the mist blocking the passage (screen above). Activate the Clear Skies Shout and use it to dispel any part of the mist. The other heroes should follow your example.
Alduin will soon cause the mist to return, so use the Clear Skies Shout once again. Repeat this one more time to get rid of the mist for good and you will be able to begin the final fight (screen above). I'd DIFINITELY suggest saving your game here!!
New main objective: Defeat Alduin
The heroes of Sovngarde will of course participate in the final battle, so you will have three allies on your side. Don't however that slaying Alduin will be easy. Most of all, you need to be ready for the dragon to throw large boulders onto the battlefield (screen above) and occasionally breath fire.
The key to success will be of course forcing Alduin to land by using the Dragonrend Shout. Remember to always wait for a good moment o use the Shout, so you don't waste any charge. After successfully using it, wait for the dragon to land somewhere in the area (screen above).
Only afterwards should you move to attacking Alduin. If you prefer range attacks, you need to aim around the dragon's head. If you on the other hand prefer melee combat, try to approach him from the side (screen above) or from the back, as otherwise he would deal you massive damage.
Now you just need to keep repeating the above actions, so alternate between pulling Alduin down and attacking him once he lands. Of course be sure to keep an eye on the health, magicka and stamina bars and regenerate them when needed. Keep fighting until Alduin loses all of his health. Watch a flashy cinematic showing the death of Alduin and absorbing his soul (screen above).