In a large bowl or pitcher, combine the granulated sugar, orange juice, cranberry juice, pineapple juice, and lemon juice. Stir well until the sugar has fully dissolved.
Add the triple sec, light rum, orange slices, and fresh cranberries. Stir gently to combine. Cover and refrigerate for 1 to 2 hours to allow the flavors to blend.
Just before serving, pour in the lemon-lime soda and stir lightly. Serve over ice if desired and garnish with fresh mint.