In a small saucepan set over medium-high heat, combine the balsamic vinegar and sugar. Bring the mixture to a boil and continue cooking it, scraping down the sides as needed, until it has reduced and is the consistency of syrup, about 5 minutes. (It will thicken as it cools and only yield a few tablespoons.) Set it aside to cool while you prepare the salad.
Cut the watermelon into cubes or use a melon baller and scoop it into balls. Add it to a large bowl.
In a small bowl, whisk together the lime juice and olive oil with a pinch of salt and pepper. Pour the dressing over the watermelon, add the chopped mint and feta cheese, and toss to combine. Drizzle the salad with the balsamic syrup and serve immediately.
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