Pour 4-5 cups of water to a large pitcher. Add the tea bags, cover pitcher with lid and refrigerate overnight (or at least 12 hours for maximum flavor).
Make a blueberry syrup by combining blueberry juice, sugar and 1/3 cup (80 ml) water in a small saucepan. Stir to dissolve and bring to a simmer over medium heat.
When the sugar dissolves completely, after about 1-2 minutes, remove syrup from heat and transfer it to a heatproof jar. Let cool completely, then store covered in the refrigerator for up to a week.
To make the iced tea, first discard the tea bags. Then stir in bluberry syrup, until it dissolves and top up the pitcher with as much ice as possible. Serve iced tea over ice with lime slices and mint.
Notes
To make an iced tea that isn't as sweet, only use 1/2 of the syrup and store the rest for later.