Combine water and sugar in a small pot over medium heat. Whisk until sugar dissolves in the water. Add 12 mint leaves. Bring to a boil and whisk for 1 minute. Remove from heat and let cool, about 30 minutes.
Place lime and 12 mint leaves in a glass; mash together with a muddler to extract flavors. Add fresh mango; muddle until combined. Stir in 2 tablespoons of the mint simple syrup. Stir in coconut rum. Fill glass with ice and top with club soda. Stir 1 more time to distribute flavors.
