The Greater Good
This begins immediately after confirming Rufio's death in 'Sic Semper Tyrannis'
Return to shore and speak to Amunet, atop a burnt-out roof.
She voices concerns about Gamilat. Follow her to his camp of rebels.
The minstrel is here, but tipping him does nothing. Instead press forward and up- your scan will indicate the one guy willing to talk to you about Gamilat.
He'll give you the information you need, but before you leave, you might loot the carbon crystals from Gamilat's tent.
Speak to Amunet as you leave or don't, but either way you'll find Gamilat in a water-surrounded platform at Shur Quarry.
Your conversation ends in a fight to the death (I suppose there's a reason it's not called Personal Counselor's Creed).
Gamilat is a powerful fighter, but you have an ace in the hole here. Whenever things start going badly for you- jump in the water.
He'll try to hit you with missile attacks, so just stick real close the platform, and let Bayek heal. When you're ready to re-engage, take cover behind the arrow-refill on the lower platform.
A headshot will send him running down the ramp to confront you, and from there it's rinse and repeat.
You'll probably have to do this a number of times to wear him down, but when he finally falls, confirm his kill to enter the long, final cutscene, and the end of this DLC storyline.
And also, incidentally, the end of the mission.
You can still adventure through the Sinai completing other quests. The original Bureau is gone, though you can still read the scrolls in the antechamber. Note also that your current hideout has a few carbon crystals to loot.