Bottle Caps return to Pokemon Brilliant Diamond and Shining Pearl as a way to max out your partners' stats.
There are two surefire ways to obtain Bottle Caps in Pokemon Brilliant Diamond and Shining Pearl. Both of them are going to require you to play through a large portion of the game.
Once you have unlocked the Battle Tower, you can purchase Bottle Caps with the BP earned from battling. As well, a Pokemon with the Pickup Ability has a small chance of finding one.
How to get Bottle Caps in Pokemon Brilliant Diamond and Shining Pearl
The Battle Tower is an area in Pokemon Brilliant Diamond and Shining Pearl where you can test out your battling skills against some of the toughest NPC opponents in the game.
Each victory earns you a certain amount of Battle Points or BP. BP can then be used to purchase a variety of items from different vendors found in the lobby of the Battle Tower.
One of those vendors will sell you Bottle Caps. Bottle Caps can be purchased for 25 BP. This can only be done after you have obtained the National Pokedex in Brilliant Diamond and Shining Pearl.
To do that, you need to have beaten the Champion and entered the Hall of Fame. Then, you must have all 150 Sinnoh Pokemon seen and completed the regional Pokedex.
Pickup is an Ability that a handful of Pokemon can have. Those Pokemon are Munchlax, Aipom, Ambipom, Pachirisu, Zigzagoon, Phanpy, Meowth, Teddiursa, and Linoone.
After a battle, if the Pokemon is not holding an item, they have a 10% of picking up a random item. If the Pokemon is higher than level 71, there is a 1% chance that if an item is picked up, it will be a Bottle Cap.
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This method is nowhere near as easy and guaranteed as grinding out the Battle Tower is. Still, you could get lucky and end up with a couple of free Bottle Caps if you have Pokemon with Pickup in your party.