Chop the cucumbers into small pieces. To a large glass or small bowl, add the blueberries and chopped cucumbers. With a muddler, crush until combined. Add 3-4 mint leaves and gently press down with muddler.
Scoop half of blueberry-cucumber mixture into bottom of a cocktail shaker. Add 2 tablespoons lime juice, 2 tablespoons simple syrup, and 1/4 cup gin. Fill shaker with ice and shake 30 seconds. Double strain into a chilled martini glass or cocktail coupe. Garnish with mint leaves. Repeat process with remaining ingredients for second serving.
Tip: To make a simple syrup: In a medium saucepan, combine 1/2 cup sugar and 1/2 cup water. Bring to a boil, stirring until sugar has dissolved. Let cool. Transfer to a glass jar or container and seal tightly. Simple syrup will keep for up to 1 month.