You have once again found the wrong type of crystal, but Ceana knows where you can get the type that you need.
This quest is available if you have completed the quest History Repeating, and have reached level 43.
Starting the Quest
Talk to Ceana in Aleport in Western La Noscea to begin the quest.
Speak with Hedyn in Gridania
Go to Gridania and use an aetheryte to go to Mih Khetto's Amphitheatre. Go west and talk to Hedyn.
Use the True Heart to Lure Out the Crystal Bearer
Use an aetheryte to go to the Central Shroud via the White Wolf Gate (if you haven't unlocked it, talk to Tyoh Moui at the Gridania Aetheryte Plaza and do the blue quest "Broadening Horizons").
Go south and then east and go across the bridge. Go toward the quest destination and make your way down the spiral to reach the cavern below. Find the glowing purple Destination, then dismount and target it, then you can either examine or target it and use the True Heart on it from the Key Items section of your inventory, or you can target it and use the icon to the right of the quest name in your list of active quests. The Crystal Bearer will appear. Kill it.
Deliver the Corrupted Crystal to Hedyn
Go back to Gridania and use an aetheryte to go to Mih Khetto's Amphitheatre. Go west and talk to Hedyn to hand over the crystal and complete the quest.
Next Main Scenario Quest
After you complete the quest, talk to Hedyn to accept the next quest: Better Late than Never.