It's probably an objective goal. If you are a big role model and excellent Pokemon Trainer, you could be considered a Master. So, hypothetically, you'd have to beat at least one Champion and do some other things that would make you famous (such as save the world or complete the Pokedex).
In my mind, the only ingame character that has obtained this distinction is the MC of XY. They not only saved the world and beat the Champion, but they had all of Kalos acknowledge them as their savoirs. I feel like the Honor of Kalos was pretty much saying that they considered you a Pokemon Master.
3DS FC: 4596 9948 4995 (Fighting Safari with Machoke, Throh, and Riolu) Shiny Value: 695 (PM me to hatch your shiny- I won't ask for anything in return!)