On this page of our guide to Greedfall, you will find a detailed description of The Sky's Teeth main quest.
After the cutscene, you will fight Vinbarr. First, the king will be in his human form, which is weak and should not give you any trouble. After some time Vinbarr turns into a beast - Nadaig Meneimena.
The battle is similar to that with other Nadaigs. You should focus on dodging and keep an eye on sword swings/charges. You should also remain vary of his physical attacks, because the opponent performs strong sword attacks. You have your comrades to aid you, so the boss is likely to focus on them - attack him in the back.
After taking care of Vinbarr, go to Constantin. Then get him out of the stone prison, and you will see a cutscene. The quest is complete, you get +2000 XP and move to New Serene. Go to a meeting with the cousin of the main character, and you will start a new quest - The New High King.