Korrina's gym is dominated by fighting-type pokemon. It will help bringing in psychic and flying pokemon to get on your offensive. The arena itself is wide and open. To completely raise the railing that will take you to the middle platform, you have to seek out and defeat the gym trainers who are scattered in the area. Some of them won't actively call you t o battle so you have to talk to them in order to challenge them.
Roller Skater Rolanda (Prize Money: 928)
Roller Skater Kate (Prize Money: 896)
Roller Skater Dash (Prize Money: 960)
Roller Skater Shun (Prize Money: 864)
After defeating the gym trainers, the railing will be complete. You can go back to the pokemon center to get your party healed up. When ready, just slide over the railing to reach the central platform where Korrina will appear to battle you.
Gym Leader Korrina (Prize Money: 5,120)
Rewards:
Korrina will inform you to meet up with her at the top of the Tower of Mastery. For now, visit the Pokemon Center to heal up then proceed to the Tower as she suggested. Once inside the tower, make your way to the ramp. Continue heading to the top but stop by the third room. Talk to the guy inside to get TM47 Low Sweep.
Head to the top of the tower to finally meet up with Korrina. Here, she'll hand you over your own Mega Ring. The Lucario that has shown interest with you during your last encounters will side with you. Korrina will then offer a battle.
Successor Korrina
In this battle, you'll be using your very own Lucario. A new option will be available in your battle menu. Press the Mega Evolution option then select an attack to transform your Lucario into a Mega Lucario. Since you'll land the first strike, you should be able to defeat the opposing Lucario on your next turn. After the battle, you'll have the option to bring Lucario with you or not. After deciding, you can go down the tower and be on your way.
Head to the pokemon center and heal up. Once done, head to the right and look for the hiker that's looking for something. Talk to him and hand over the intriguing stone Tierno gave you earlier. The man will give you a Sun Stone in return. Head to the city exit and your neighbor will catch up and give you HM03 Surf. Now continue forth to reach Route 12.