For this achievement you'll need to have 3 special mounts for your lords/heroes. This achievement can be obtained in both the Eye of the Vortex campaign and Mortal Empires campaign.
Some lords and heroes have special mounts in their skill tree, the top yellow one. Not all heroes and lords have this ability, but most do, especially legendary lords. As it's a skill, it means the lord/hero needs upgrading to a certain level by winning battles or performing campaign actions, and having a skill point available.
Special mounts include dragons, great eagles, chariots, warsphinxes, dinosaurs, etc. Most races have these, including High Elves, Lizardmen and Tomb Kings. After you have three lords/heroes with these kind of mounts the achievement should unlock.