This page of the guide to Elex 2 contains a walkthrough of the Elex Purity mission, which you will receive during the Adversity quest. Your main goal is to defeat the Skyands that attack the Depository.
Conversation with Ekrom
First, go to the Depository (HQ of the Albs) and talk to Ekrom. Ask whether the faction faces any problems, and you'll find out that the city has been attacked by the Skyands.
Fighting the Skyands
The enemy locations will be marked on your map - they are in front of the Depository. The Albs will not take part in this fight, so make sure you take a companion with you fo some help. You have to kill 15 Curators, as well as the group leader. The mission will end automatically when you kill all enemies. You don't have to go back to Ekrom - you won't get any additional reward.