Dire Prey

I did severel quests without getting this quest completed - tried severel different types looking for what appeared to be elite and rare.

A wq starting with DANGER:... completed it for me.

Edit: Did a 'WANTED' wq for one of the other hatchlings and it didn't get completed, so it appears the DANGER quests are the ones to go to...

All world quests prefixed with 'DANGER: ' are considered Rare Elite World Quests and will grant credit.

There are also quests which lack the prefix but should also give credit.
_{I personally had success with Sick of the Sycophants in Suramar.}

List of quests with type 'Rare Elite World Quest' from the Wowhead database:

• 
  
• Azsuna

DANGER: Arcanor Prime
DANGER: Chief Treasurer Jabrill
DANGER: Fjordun
DANGER: Immolian
DANGER: Jade Darkhaven
DANGER: Karthax
DANGER: Kosumoth the Hungering
DANGER: Lysanis Shadesoul
DANGER: Marblub the Massive
DANGER: Mortiferous
DANGER: Sea King Tidross
DANGER: Stormfeather
DANGER: The Whisperer
DANGER: Torrentius
DANGER: Valakar the Thirsty

A Friend of My Enemy
A Giant Murloc Problem
Aquatic Assassination
Demonicide
Evil Has Many Legs
Felled Experiment
Hate the Hatecoil
Nagana Happen
Shell Out Some Pain
The Felsworn Must Fall
Watery Graves

• Highmountain

DANGER: Ala'washte
DANGER: Defilia
DANGER: Durguth
DANGER: Mawat'aki
DANGER: Ormagrogg
DANGER: Oubdob da Smasher
DANGER: Xavrix

Lords of the Hills
Lords of the Hills

• 
  
• Stormheim

DANGER: Aegir Wavecrusher
DANGER: Boulderfall, the Eroded
DANGER: Captain Dargun
DANGER: Den Mother Ylva
DANGER: Fjorlag, the Grave's Chill
DANGER: Huntress Estrid
DANGER: Lagertha
DANGER: Rulf Bonesnapper
DANGER: Runeseer Sigvid
DANGER: Soulbinder Halldora

Culling the Storm
Sacred Bones
The Helarjar Have Surfaced

• 
  
• Suramar

DANGER: Auditor Esiel
DANGER: Az'jatar
DANGER: Colerian, Alteria, and Selenyi
DANGER: Magistrix Vilessa
DANGER: Oglok the Furious
DANGER: Scythemaster Cil'raman
DANGER: Sorallus
DANGER: Volshax, Breaker of Will

Consolidating Power
Sick of the Sycophants
Stelleris Shakedown
Unspeakable Collaborators

• 
  
• Val'sharah

DANGER: Ealdis
DANGER: Harbinger of Screams
DANGER: Kathaw the Savage
DANGER: Lytheron
DANGER: Malisandra
DANGER: Nylaathria the Forgotten
DANGER: Rabxach
DANGER: Shalas'aman
DANGER: Witchdoctor Grgl-Brgl

Blue = rare, golden dragon = elite, so you want a world quest that has both.

Qualifying quests are labeled as "Type: Rare Elite World Quest" in the quick facts section in the upper right on wowhead. Or check this list.

Or you could just get credit for no apparent reason as I once did.