Bring water to a boil in a small saucepan; remove from the heat, add tea bags, and let steep 5 minutes. Remove tea bags and stir in sugar until dissolved. Transfer to a pitcher, add peach nectar, and stir to combine. Chill in the refrigerator for at least 1 hour.
Fill tall glasses with ice and then pour peach tea over, leaving some room at the top for the whiskey. Stir in 1 shot of whiskey to each glass and garnish with a peach slice and fresh mint sprig.