After you reach the heart of the Aetherochemical Research Facility and witness the archbishop's actions, you follow him to the Singularity Reactor.
How to Unlock
The Singularity Reactor 8-player trial is unlocked by completing the level 60 dungeon Aetherochemical Research Facility.
Defeat King Thordan
Avoid the circle attacks and puddles. Thordan sometimes casts Ancient Quaga, which damages all players.
At 80%, he will begin summoning his knights, starting with Ser Janlenoux and Ser Adelphel. Avoid their line attacks and stay away from the white orbs to avoid their explosions. Afterward, Ser Vellguine will create a large line attack across the area.
At 55%, Thordan casts The Dragon's Eye, and afterward will sometimes cast The Dragon's Eye, a gaze attack. Turn your character away from Thordan when he uses The Dragon's Gaze.
Ser Hermenost will create three towers near himself. Make sure that there is at least one player in each tower. If a tower does not have a player in it, everyone will be inflicted with Paralysis.
Ser Haumeric will mark all players with ice circles. Players should go to the edges of the area and avoid overlapping other players' circles. The ice circles will create ice puddles on the floor that inflict Heavy on those who step on them. Dropping them at the edges will keep them out of the way.
At about 15%, Thordan leaves his sword in the field and a number of his knights appear. Dodge the fire attacks, stand in the tower circles, Kill Zephirin before he can finish casting Sacred Cross. Keep Janeloux and Adelphel away from each other to prevent them from strengthening each other.
Avoid standing near the dark red and black circles that appear on the floor. They will grow, then will inflict damage on anyone standing on them.
When Comet Circles and a Meteor Circle appear around the area, destroy them as quickly as possible. At the same time, you will need to dodge the concentric attacks that Ser Guerrique casts around himself. The cone behind him is safe.
When Thordan reappears, he will repeatedly knock back all players, then will raise his sword and use Ultimate End, a high-damage spell that hits all players. Players can stack together and use shields and regen spells to prepare before he raises his sword.
Afterward, he receives a Damage Down status and targets random players with weak attacks and can be easily defeated. Be sure to watch the cutscene after he is defeated.
Completing the Quest
Defeating the boss will complete one of the quest objectives for the Main Scenario Quest Heavensward.