Cut each lime in half, then cut each half into 8 pieces. Place 12 pieces of lime in each of 4 double old-fashioned glasses (or other 12-ounce glasses.) Sprinkle 2 tablespoons of sugar into each glass. Using a muddler (or the butt end of a large wooden spoon), mash the limes into the base of the glass until the sugar is dissolved, stirring occasionally. Fill each glass with 1 1/2 cups of the ice and 1/4 cup of Cachaca. One glass at a time, transfer the contents of the glass into a shaker, and invert the glass onto the top of the shaker to act as a lid. Shake the glass and shaker together to combine the sugar and Cachaca, shaking until well-chilled. Lift the glass from the shaker, and pour the contents back into the glass. Repeat the process with the remaining 3 glasses.
Garnish with a slice of lime or a sugarcane swizzle stick if desired.
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