Press the cucumber slices against the inside of three or four glasses and add ice to help keep the cucumber slices in place. In a cocktail shaker or a large jar with a tight-fitting lid, muddle the chopped dill, agave syrup, lemon and lime juices and water until the agave syrup has dissolved.
Add the cucumber juice and some ice. Cover and shake well. Strain into the prepared glasses and top with club soda. Garnish with the dill sprig.