No RPG is complete without a dialogue pop quiz and you're going to get a deadly one when you try to obtain Mythal's essence in Dragon Age: The Veilguard. If you collect all the wolf statuettes to complete the Regrets of the Dread Wolf quest, Morrigan will have a chat with you about all the things you learned from Solas' memories.
Along with a lot of other lore about Morrigan's history and relationship to the elven gods, she suggests that you should hunt down a fragment of Solas' former partner in godhood Mythal. This essence of Mythal could be useful in the future, she suspects, but you're going to have to convince Mythal to trust you. Morrigan's advice on the matter is that Mythal will "demand respect but detest flattery" and "appreciates righteous anger but will not tolerate pity." If that's a little too vague, I've tested out all the options so you can easily convince Mythal to join your cause.
The easiest way to obtain Mythal's essence is to complete Bellara's full personal quest first. You can tell Mythal "I want your help," then "We must stop the gods," and finally "We stopped Anaris" to instantly win her favor without completing the rest of the conversation.
Essentially, Mythal will allow you to convince her to help you by giving your arguments on four different topics: the blight, the gods, your own worthiness, and having Solas on your side. Some answers will lead to an instant fight with Mythal, but she transforms into a level 45 dragon so I don't recommend that. Among the other answers, some are better than others. Your goal is to be convincing enough across those four topics to win Mythal's support.
In your conversation with Mythal, you'll get to address four different topics to convince her to assist you. I don't know what the actual under-the-hood math is, but based on all my testing, you need to gain six 'points' in the conversation, at which point Mythal will immediately relinquish her essence.
You can achieve that with the instant win talking point "We must stop the gods" followed by "We stopped Anaris." Or you can give the best answers (two 'points' each) to three different subjects.
Your first dialogue choice must be "I want your help." Both other options lead to an instant fight with Mythal as a dragon. Here are all the dialogue options for the four topics of conversation, the best answer in bold for two points, a less optimal answer for one point, and the option you should avoid unless you want to fight.
Again, your goal is to get six points, using the dialogue choices below:
"We must stop the blight"
"We must stop the gods"
"We are worthy"
"Solas is helping me"
