For this achievement, you must win a battle with each companion, including Simon, Thea, Gaul, Ogden, Kora, and Eleanor.
This unlocked for me after completing the last of each of the companions’ first side missions, as they’ll join you throughout the mission. Just make sure you complete at least one battle with each of them before the Side Story ends! Victories with Simon happen naturally as part of story progression.
Alternatively, you can use the Change Battle Allies option on the pause screen (under your current companion) to select your desired companion.
Once you’ve achieved victory with all 6, you’ll have your achievement!
Like many of these achievements, you can check your progress in your Ranger Records by pausing the game, navigating to “Ranger Files” (one tab to the right), and then selecting the Ranger Records dossier (the red one on the right). The Horn of Victory medal is the third medal on the third row and will show “All” when completed (and “6 Person(s)” in the top-right counter).