Steep the hibiscus and green tea bags in a pitcher with hot water until brewed. Set aside and allow to cool completely.
In a blender, add the freshly squeezed lime juice and cooled tea and blend. Add 1 cup of ice cubes one by one until well incorporated.
In tall glasses, add the rest of the ice cubes and several blackberries in each glass.
Pour the blended mixture in, add a straw and enjoy while chilled.