In a large pitcher or punch bowl, combine the pineapple juice, dry ginger ale, and sparkling apple juice. Pour in the lime juice and stir thoroughly until well blended.
Transfer the punch to large bottles with a secure closure if storing ahead of time, and refrigerate until well chilled. Alternatively, place the entire pitcher in the refrigerator if space allows.
Just before serving, remove the punch from the fridge. Add a generous amount of ice to keep it crisp and refreshing. Garnish with fresh mint leaves, juicy cubes of pineapple, sliced oranges, and peach wedges. Serve immediately for a vibrant and fruity refreshment.