Trim the ends off the lime and halve it lengthwise. Cut each half into 8 slices. In a cocktail shaker, using a wooden spoon or a pestle, muddle the lime with the 1/4 cup of sugar until juicy and the sugar dissolves. Add the cachaça and the crushed ice and shake for 10 seconds; taste and add more sugar if desired. Pour into an old-fashioned glass or tumbler and serve.