But to Polygon, Masuda mentioned that the post-game contains various Master Trainers, some really powerful trainers that you will have to power up your Pokémon to defeat
Edit @ 17:14: The Spanish site, Vandal, elaborates on this further and states that there are 151 Master Trainers, one for each of the original Pokémon. Each of these will focus on the species of Pokémon at a high level so you have to defeat them all. So if you find the Squirtle Master Trainer, you will defeat him and gain the title