Add fresh blackberries, sugar, lime juice and mint leaves to a cocktail shaker. Shake vigorously until the blackberries and mint leaves have pulverized. No muddler needed.
Add white rum and fill the cocktail shaker half way with ice. Shake again.
Pour the contents of the shaker into a tall glass filled with ice. No need to strain the ingredients. Top with club soda. Garnish with more mint and blackberries. Enjoy!