There are a total of 7 unique mounts required for this achievement, including:
1. Caragor - unlocked using the Call Mount skill.
2. Dire Caragor - unlocked using the Dire Caragor skill upgrade.
3. Graug - unlocked using the Graug Call skill upgrade; level 30 required.
4. Drake - unlocked using Dragon Song skill upgrade awarded for completing the Carnan quests.
5. Poison Graug (Elemental) - Nurnen - Available near the middle fast travel point. Keep advancing time until it spawns nearby and them break and dominate it.
6. Fire Graug (Elemental) - Gorgoroth - Available near the cave/tunnels near the left middle. Keep advancing time until it spawns nearby and them break and dominate it.
7. Ice Graug (Elemental) - Seregost - Available near the ice lake caves on the left of the map. Keep advancing time until it spawns nearby and them break and dominate it.