In Lord of the Hunt mode/DLC, you must complete four secondary (white) missions to unlock the fifth. You'll also need to complete some main storyline missions. In the fifth secondary mission, you will unlock the Blazing steed power. On a Caragath, kill enemies to charge the power, then press
together to activate the blazing steed power. The achievement will unlock immediately, you do not need to finish the mission.
The four secondary missions are "Heaving Rampage","From Hunter to Hunted","Belching Monstrosity", and "A Feast of Flesh." You can then earn this during "Beast Master." You can continue to play Lord of the Hunt after completing all story missions.