Combine the granulated sugar, water, peach juice, and quick-cooking tapioca in a medium-sized saucepan. Heat the mixture over medium-high heat, stirring frequently to dissolve the sugar and prevent the tapioca from sticking. Bring it to a rolling boil and let it cook for about 12 minutes, continuing to stir to ensure the tapioca thickens evenly.
Once cooked, remove the saucepan from the heat and transfer the mixture to a large bowl or container. Stir in the orange juice until fully blended, then cover and refrigerate. Allow the mixture to chill for at least 4 hours or up to several days to ensure it is thoroughly cooled and the flavors are well developed.
Just before serving, gently fold in the mandarin oranges with their juice, the drained peaches (cut into bite-sized pieces if needed), and the fresh strawberries, raspberries, and blueberries. Mix lightly to avoid crushing the delicate berries. Keep the fruit soup chilled and serve within an hour to preserve the freshness of the added fruits.