Getting to the top is a rather monstrous task for Pokémon trainers at the beginning in Brilliant Diamond and Brilliant Pearl, but after a certain event in the game's story, you can climb rocky cliffs like a beast. Here's how to do it.
To unlock the ability to climb rocky cliffs, you'll need to get yourself a bike. Unfortunately, while in Oreburgh, you are out of luck. Instead, you have to go a long way from Jubilife to Floarama, through the forest of Eterna and then the city of Eterna to find one of these elusive bikes.
Once there, you find that the bicycle seller is nowhere to be found in the city. He has disappeared. His daughter told you that he was taken by Team Galaxy. To bring him back, you will need to enter the building north of Eevopolis.
You'll need Cut to break through the trees blocking your path to Team Galaxy's base. To use Cut, you will need to beat the Echo City gym. You will receive it from a random stranger as you approach the Team Galactic high building.
Once inside, defeat the Team Galaxy henchmen (remember to go to the Pokémon Center to heal yourself first) and go upstairs. You'll find the bike vendor trying to save his Clefairy, which was stolen by the evil group. Defeat the commander there and, once the fight is over, meet the bike salesman in his shop. It is north of the Pokémart and south of the Pokémon Center.
Now that you have the bike, you can climb the rocky cliffs. Press Button B to shift gears, and when you see the wheels twinkle, you know you're at the right speed to climb the obstacle.