After you witness the fate of the Qalyana, you have no choice but to confront Sri Lakshmi.
How to Unlock
The 8-player trial Emanation is unlocked by the level 67 Main Scenario Quest The Lady of Bliss.
A Note About Vril
You have a Duty Action in this battle called Vril. It will be displayed on screen as an action button, separate from your hotbar/crossbar.
If your Vril count is 0, make sure to get a charge of Vril by walking through one of the glowing bubbles that appear whenever Lakshmi casts Stotram.
Vril should be used at specific times in the battle that will be explained below.
At the beginning of the battle, defeat the two Dreaming Kshatriya. Make sure to move away from them if they cast Inner Demons, a circle attack centered on the enemy.
After you defeat the Dreaming Kshatriya, focus your attacks on Lakshmi.
Hand of Grace places a cross-shaped marker on two players. These players should move to an edge of the area and make sure not to overlap any other players marked with a cross-shaped marker. Once you have moved to an edge, it is best to stay still rather than trying to move your line markers away from other players. Staying still will allow the other players to find a safe spot away from you.
The Pull of Light is a high-damage attack on the player highest on the enmity list.
Hand of Beauty marks two players with circles that follow them. The marked players should avoid overlapping each other with their circles, and should move to an edge near each other and away from other players. When the attacks hit, they will leave behind puddles that will grow larger. Move away from them.
When Lakshmi becomes untargetable, wait a few moments, then use your Vril Duty Action to activate Vril status. There will be a cutscene, and if you did not use Vril before the cutscene started (when Lakshmi blew a kiss), or you used Vril too soon and your Vril status runs out before the cutscene ends, you will die.
After the cutscene, use Vril whenever Lakshmi is casting Divine Denial, which makes the entire platform glow. This attack will knock you away from the center of the area, and if you do not use Vril, you will be knocked back much farther. Knockback-prevention moves do NOT prevent you from being knocked back by this attack, so you must use Vril.
The Path of Light will target the player who is second-highest on the enmity list with a blue spinning marker over their head. This player should turn Lakshmi to face away from other players to prevent her from hitting them with this attack.
The Pall of Light targets a random player with a stack marker. Players who are NOT currently marked by other attacks (such as the cross-shaped line attack markers) should stack together with the player who has the stack marker.
Alluring Arm will simultaneously mark two players with cross-shaped line attack markers and two other players with circle attack markers that follow them. All of the marked players should move to an edge without overlapping each other with their attack markers, and the two circle-marked players should stay near each other without overlapping each other with their circles. The marked players should then stay still to allow the other four players to find safe spots. After the circle attacks hit, players need to run away from the growing puddles as before.
Completing the Quest
Defeating the boss will complete one of the quest objectives for the Main Scenario Quest The Lady of Bliss. There will be a cutscene. This one is important, so it is recommended to watch it either now or via the Unending Journey in an inn room.