Meteor Draco is among the most powerful moves a Dragon-type Pokémon can learn in Pokémon Brilliant Diamond and Shining Pearl, so if you're incorporating any Dragon-type into your team, it's a move you might want to consider. However, it is not learnable by leveling up; it can only be taught to you by one of the game's Move Tutors, which is only accessible after some footwork.
The Move Tutor is an elderly woman named Grandma Wilma who resides in a house located on Route 210, but there are a few things you will need to do to get to the house. First, you'll need to take out the Psyduck barricade that prevents you from accessing much of Route 210, which also requires you to defeat the fourth Gym Leader, Crasher Wake. Additionally, you'll also need the MT100 Rock Climb, which isn't usable outside of battle until you defeat the seventh Gym Leader, Candice.
As you travel right on Route 210, you should come across a rock face that you can climb. Do this and you'll end up in a narrow pit with another climbing wall directly in front of you; climb this wall and you will arrive at Grandma Wilma's house. She enters the building, she talks to Wilma, and she will offer to teach "the best Dragon-type move" to one of your Pokémon. She accepts her offer from her, selects which Dragon-type Pokémon you would like to learn Draco Meteor and will now be able to use the move.
The attack deals heavy damage, but also drastically reduces the user's Special Attack stats. Any Dragon-type Pokémon is able to learn this move, but its Friendship level must be at its maximum to be able to do so. If you're having trouble with this, check out our guide on how to quickly raise your Pokémon's friendship level.