2. Complete Tier 13+ Maps with The Searing Exarch's Influence
Once The Black Star is defeated, you will need to complete Tier 13 or higher maps that have The Searing Exarch’s influence. This will gradually unlock the ability to challenge the Searing Exarch in a story version of the fight.

As you progress through the maps and complete Tier 13+ maps with The Searing Exarch’s influence, you will eventually receive an invitation to fight him in the story version of the encounter.

3. Obtain the Invitation
After completing the required maps, you will receive an invitation to face the Searing Exarch. This invitation can be slotted into your Map Device, where you can fight The Searing Exarch in a controlled encounter.

Invitation drop: This occurs after completing Tier 16 maps with The Searing Exarch’s influence. Once you've completed enough of these maps, you will earn an invitation to the boss fight.

Omniscient Voidstone: After defeating the Searing Exarch in the story version, you will receive an Omniscient Voidstone as a reward. This Voidstone can be slotted into your Atlas to increase the tier of all maps you run, effectively boosting the difficulty and rewards of your mapping experience.