The next activity in the Special Demo is the Battle Challenge, even though you can actually participate in it before the Capture Challenge. Of all the people found on Ten Carat Hill, there are three mystery trainers looking for a battle. Since there are only about six of seven people found in the area, it won't take to long to find them. However, you may need to ride Tauros and smash rocks to find some of them.
The three trainers are pretty easy to defeat, especially since you have Greninja on your side. Again, much like the wild Pokemon found in the Special Demo, these trainers will only have either Yungoos, Pikipek or Rockruff. They will, however, be at stronger levels than what you saw with Team Skull, so be prepared for a little more of a challenge.
After defeating the very last trainer, you will be given a rare Star Piece. This expensive item can also be sent to your Pokemon Sun or Pokemon Moon Game via the Pokemon Link.