In my opinion, easiest specs to get the mount are:
- Twins: Frost Mage
- Closing the Eye: Frost DK (Arms is close)
- God Queen: Enhancement/Arcane
- Agatha: Any (Fury and Unholy are a bit tougher than the others)
- Fel Totem: Windwalker
- Healer: Paladin
- Tank: Monk/DH/War