Pokemon Swarms are back in Brilliant Diamond and Shining Pearl, but it's a feature that needs to be unlocked.
The Swarms mechanic was seemingly abandoned when Pokemon X and Y released. Since these recent games are a remake of Generation IV, however, it has been brought back.
The mechanic isn't available right away and you can't encounter Swarms of Pokemon in Brilliant Diamond and Shining Pearl until you've beaten the Champion and obtained the National Pokedex.
How to battle Pokemon Swarms in Brilliant Diamond and Shining Pearl
Defeating the Elite Four, becoming Champion, and unlocking the National Pokedex is the first step to unlocking the Swarms feature in Brilliant Diamond and Shining Pearl.
After you have done all of that, go to Sandgem Town and enter the house of Lucas or Dawn, whichever is your ally/rival in your playthrough. Their house is right under the Pokemon Center.
Speak to Lucas/Dawn's sister and she will inform you of a Pokemon Swarm. Head to whatever route number she mentions and the creatures will be seen popping in and out of the grass.
Walk into the tall grass and you will end up encountering one of the Pokemon from that day's Swarm. You can battle them all for some great EXP and catch one if you need to add it to your National Pokedex collection.
The Swarm changes its type of Pokemon and location every single day. You can talk to Lucas/Dawn's sister to find out exactly which species and where the Swarm is on a specific day.
Alternatively, you can press the menu button on your Nintendo Switch and look at the textbox that gives you hints on what to do next. This textbox can also be seen when viewing the Town Map.
Since the Swarm feature only happens after the National Pokedex is obtained, you'll find that many of the Pokemon are those needed to complete the National Pokedex.
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Be sure to check back every single day so you can get your National Pokedex completed and take another step closer to becoming the "very best like no one ever was."