After you ride on the roller coasters in Nimbasa City, Elesa will arrive at her Gym.
Make your Way to Elesa
Now you can challenge Elesa, but first you have to defeat the other trainers in her gym. The gym is to the right of the roller coaster building. Be sure to talk to Clyde near the door of the gym to get your Fresh Water.
Go up the catwalk and you will encounter Beauty Nikola. She sends out a level 27 Elekid and a level 27 Flaafy.
Next, you encounter Beauty Fleming. She sends out a level 27 Flaafy and a level 27 Blitzle.
After that, you encounter Beauty Ampère. She sends out a level 27 Blitzle and a level 27 Elekid.
Finally you encounter Elesa on the stage. She has a level 28 Emolga, level 28 Flaafy, and level 30 Zebstrika. Keep in mind that since Emolga is a Flying pokémon, Ground moves don't work on it at all. Rock moves and Ice moves are supereffective on it.
When you defeat Elesa, she gives you the Bolt Badge and TM72 Volt Switch. Your picture also replaces Elesa's on the big screen.
When you leave the gym, Elesa and the supermodels ask to talk to you. Elesa tells you that you have what it takes to get all the gym badges and reach the pokémon league.