In a large heat-safe bowl, combine the peach gelatin, granulated sugar, and boiling water. Stir for 2 to 3 minutes, or until the gelatin and sugar are fully dissolved and the liquid looks smooth.
Stir in the frozen lemonade concentrate, pineapple juice, and cold water until evenly combined.
Pour the punch base into freezer-safe containers, leaving a little room at the top for expansion. Freeze until solid, preferably several hours or a day or two ahead.
About 1 hour before serving, remove the frozen punch base from the freezer. Break it apart with a fork until it has a soft slushy consistency.
Transfer the slushy punch base to a large punch bowl. Slowly pour the white soda over the top and gently fold it in so the punch stays fizzy.
Serve immediately while cold and slushy.