Place 1 cup water, the blueberries, and mint in a medium saucepan and bring to a simmer. Simmer until the blueberries start to break down and release their juices, 3-4 minutes. Remove from heat and stir in the agave. Let cool.
Pour the blueberry syrup into a large pitcher and stir in the lime juice and remaining 5 cups of water. Refrigerate.
To serve, fill glasses with ice and add some blueberries to the glasses. Pour the blueberry limeade into the glasses and garnish with lime slices and mint leaves.
Notes
If you like your drinks with a little sparkle, you can try stirring some sparkling water into your glass of Blueberry Mint Limeade.