You can either convince Mythal to give you her essence or fight her dragon form to get it during the Regrets of the Dreadwolf quest in Dragon Age: The Veilguard.
We highly recommend you convince her with the correct Mythal answers during the Regrets of the Dreadwolf quest, instead of battling her, as Mythal will assist you in the fight against the Revenant Dragon at the end of the Heart of Corruption quest if you keep her alive. As this is perhaps the hardest fight in the entire game, you're going to need all the help you can get.
If you find you've selected an incorrect answer and Mythal gets angry - don't worry, you don't have to fight her. Just reload your most recent temporary decision save from the main menu, as one is automatically created once you speak to Mythal in Dragon Age: The Veilguard.
For more help on your travels across Thedas, check out our Dragon Age: The Veilguard walkthrough.
Once you've listened to Morrigan and know the truth about Mythal, follow the quest marker to the fragmented Mythal's location where you can either fight her for her essence, or convince her you're worthy to receive her essence.
You need Mythal's essence if you want to unlock a third alternate ending in Dragon Age: The Veilguard.
As mentioned above, we highly recommend you try and convince Mythal to hand over the essence instead of fighting her, as this means she'll be around to give you a helping hand against the Revenant Dragon in the Heart of Corruption side quest.
When you're ready to convince her, here's the correct Mythal answers in Dragon Age: The Veilguard:
There are alternative dialogue options you can pick to convince Mythal, but this is what worked for us.
Once you receive Mythal's favor and her essence, the Regrets of the Dreadwolf side quest is complete, and you'll be able to pick a third alternative ending during the closing moments of the game. As you didn't fight her, you also have Mythal's favor, meaning she'll swoop down and assist you against the Revenant Dragon at the end of the Heart of Corruption side quest.
All the best in the rest of your travels through Thedas!