Using your finger tip, rub the rim of a tumbler glass with mint syrup. Sprinkle a small amount of sugar onto a small plate, and turn the glass upside down onto the plate to sugar the rim. Repeat the process on the second glass.
In each glass, place 2 quarters of the lime, 1 tsp of sugar, 1/4 of a whole peach, and 1 sprig of mint. Muddle together so flavors blend.
Add enough ice to leave about 3/4 of an inch from the top of the glass, and then add 2 shots of Cachaca and 1/2 shot of mint syrup to each glass. Stir with a spoon until blended.
Garnish the edge of the glass with peach slices and top the drink with a sprig of mint.