You can obtain Gold Bottle Cap as a reward for completing the Academy Ace Tournament. The Academy Ace Tournament is unlocked after completing the game and defeating all 8 Gym Leaders in a rematch..
A variety of items are rewarded to the player for each successful run at the tournament, with Gold Bottle Cap included in the reward pool.
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Golden Bottle Caps can be obtained through the Porto Marinada Auction. Players will have to put down the winning bid in order to unlock them.
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These were the only two locations I could find. They are rare.
