This quest begins shortly after you finish your conversation with Alustin during the "Polar Opposites" quest, once you are teleported outside the Axiom Archive.
After the blinding light subsided, you found yourself once more outside the building. Restore the Abyss according to Alustin's advice.
Walk through the triangular gate ahead of you then use Axiom Force to grapple the blue glowing center part of the pedestal in front of you.
Next, use the D-pad to rotate it slowly. Continue rotating until you feel a vibration. After a moment, the floating platforms will align to form a path, allowing you to proceed.
Jump across the floating platforms to reach the next floating island.
By jumping and climbing, you will eventually reach a slightly more challenging section where you must navigate moving platforms. Wait for them to drift close to each other before leaping from one to the next.
This will lead you to the next island, where a teleporter is located. Step onto it to be transported further ahead.
By jumping across several more platforms, you will eventually reach the vicinity of another Abyss Nexus.
Just like before, simply step onto the platform to do this.
Move the floating power core to the deactivated lantern using Axiom Force.
Jump down, approach the echo / blue ghost and observe him to learn Force Palm.
Use Axiom Force to place the power cell in front of the wall...
... then use Force Palm to punch the cell into the wall.
The power supply is the giant wheel on the wall above. Climb onto the wheel, hang from its center, and then unleash Force Palm while still clinging to it.
Head up to the platform above the big wheel and approach the floating, glowing item. You will automatically collect the artifact, completing this quest. Woman in White is the next quest.
With some effort, the Abyss' balance was corrected and its original state restored.