Heat 100 ml coconut water with the sugar in a pan. Stir until the sugar crystals have dissolved. Allow to cool until use. Finely chop the tarragon.
Cut the mango into two halves along the stone. Score each half into squares without cutting through the skin. Turn out the halves with your thumb and slice off the cubes. Or use a mango slicer.
Place the mango in the food processor and add the rest of the coconut water and the rum. Blend until smooth.
Blend the tarragon with the sugar syrup with the hand blender to create a green syrup. Pour some tarragon syrup into a glass and top up with the mango shake.