This page explains how to complete the level 88 Endwalker quest "Bonds of Adamant(ite)".
This quest is available if you have completed the quest Once Forged.
Starting the Quest
Talk to Kokkol Dankkol in Labyrinthos to begin the quest.
Wait at the Destination
Teleport to the Sharlayan Hamlet (or go counterclockwise around the Central Circuit) and go to the quest icon on the map. Check on the sparkling Destination, then say Yes to proceed. There will be a cutscene.
Speak with Alphinaud
Talk to Alphinaud to proceed.
Speak with Fourchenault
Teleport to Aporia in Labyrinthos, then go to the quest icon and talk to Fourchenault to proceed.
Speak with Clarilaine
Go east to the quest icon on the map and talk to Clarilaine, and say Yes to proceed.
Speak with Fourchenault Again
Talk to Fourchenault to proceed.
Proceed to the Entrance of Thaumazein
Go east to where the orange arrow is pointing in the minimap. When you go through the doors, there will be a cutscene.
Speak with Fourchenault Once More
Talk to Fourchenault to complete the quest.
Unlock Flying in Labyrinthos
"Bonds of Adamant(ite)" is the final quest for unlocking Aether Currents in Labyrinthos. If you have completed the other Aether Current quests and attuned to the Aether Currents in the field in this area (which you can find using the Aether Compass in Main Menu > Duty > Collection in this area) you will be able to fly in Labyrinthos. However, you can't fly within the Thaumazein building.
Next Main Scenario Quest
After you complete the quest, you will need to be at least level 89 to proceed to the next quest. After you reach level 89, talk to Fourchenault to accept the next quest: Her Children, One and All.