This requires you to track quests in ATT. If you have completed a higher difficulty boss skip quest for the Emerald Nightmare ("The Emerald Nightmare: Piercing the Veil"), then ATT will still show the lower difficulty quests despite being unable to be picked up.

Relevant quest IDs:

• Mythic #22485
• Heroic #22484
• Normal #22483

The updated criteria should be:

• Quest #22485 should require Quest #22485 to be completed
• Quest #22484 should require Quest #22485 or Quest #22484 to be completed
• Quest #22483 should require Quest #22485, Quest #22484 or Quest #22483 to be completed

@Gromwind Note that I wrote it is unable to be picked up. There is no party-sync magic trick (like the breadcrumb quests in the open world) to bypass this limitation as the higher completed difficulty quest will prevent lower difficulty quests from being picked up so displaying them in the interface is redundant.

Just so happens I was in EN and actually you can party sync these quests and complete them as 4 essences drop at a time now.
For similar quests in other raids you will need to finish the lower difficulty quests first before doing the harder ones if you want them done on one character. If this is not possible your options are either to: petition blizzard for the quest or track quests account wide and do it on an alt as Gromwind said.

You can tell its a party sync quest because no waking dream reward is offered like the normal quest.

Note, this naturally means that the criteria for Cenarius on the relevant difficulties needs to be updated too (For the "Essence of Clarity")

Relevant IDs:

• Heroic #141304
• Normal #141303

Whether a quest is completed or not isn't determined by us, but by what the Blizzard API returns when the status of a quest is queried. If you track quests account wide and complete this on an alt then it will show as complete on ATT.