I need the 4th badge but the blond-haired girl says she's not there and loves the thrill of the roller coasters and I've road ever single roller coaster.
Just go to the amysement park in Nimbassa city.Walk until you reach her old gym,walk a bit more and there should be a building with round windows flashing.
Here it is : http://www.youtube.com/watch?v=eF7RWyrdwGs
You go to where her old gym was. You fight your way through to the back by riding the roller coasters. At the back you will meet another girl that tells your Elesa went back to the new gym and she will give you a Paralyze Heal. You can now go to the new gym and fight all the trainers and Elesa.
You need to go ride the rollercoasters in the old gym of Nimbasa City first. The interior should look something like this:
When you reach the end, Elesa should be there and will give you a Paralyz Heal.
If I'm not mistaken, go inside the rollercoaster building. Defeat the Beauty trainer at the end. Then she should be at the Gym.