Pokemon X and Y Walkthrough: Tower of Mastery Revisited
The guru greets you and says Korrina is waiting at the top of the tower. The Black Belt guarding the stairs will let you pass as long as you have the Rumble Badge. There are three rooms on the way up. The last room has a Psychic that gives away TM 47 Low Sweep. It's a Fighting-type move that deals damage and lowers the target's Speed by one stage.
Korrina is waiting on the tower's balcony. After she give you the Mega Ring, one of her Lucario decides it wants to join your team. It's holding Lucarionite, which lets it Mega Evolve into Mega Lucario. There's a big rainbow-colored button in the Fight menu that triggers the Mega Evolution. You can Mega Evolve a Pokemon and attack on the same turn, so there isn't a big drawback to Mega Evolving.
Keep in mind, you can also Mega Evolve the Kanto starter you received from Professor Sycamore. Head towards Route 12 on the east side of Shalour City. Serena will appear as you approach the gate to give you HM 03 Surf. It will be needed to complete Route 12.