In a cocktail shaker or sturdy jar, add the watermelon cubes and lime juice. Using a muddler or the back of a spoon, gently press and crush the watermelon to release its juice and break down the fruit—you want to extract the liquid without pulverizing the watermelon into a fine paste, as this keeps the texture pleasant. The goal is to get the watermelon juice flowing while maintaining some fruit integrity. This should take about 30 seconds of firm but controlled pressure.
Clap the mint leaves between your palms two or three times to bruise them and release their essential oils, then add them to the shaker with the muddled watermelon mixture. Add the agave nectar, apple cider vinegar, and sea salt. I find that adding these flavor components while the mint is being bruised helps them integrate better with the fresh mint oils. Stir gently to combine everything and allow the mint to steep for about 15-20 seconds.
Fill a drinking glass with fresh ice. Add a generous handful of ice to the shaker with the watermelon-mint mixture, then cover tightly and shake vigorously for 8-10 seconds. The shaking accomplishes two things: it chills everything quickly and helps marry all the flavors together. Immediately strain the mixture into your prepared glass with ice, leaving most of the pulp behind while allowing some of the flavorful liquid through.
Top the strained mocktail with the soda water, pouring it slowly to preserve the carbonation and create a nice visual effect. Stir gently two or three times to combine. I prefer Topo Chico for its aggressive carbonation, which adds a pleasant prickling sensation that elevates the whole drink. Garnish with a sprig of fresh mint and a lime wheel or wedge, then serve immediately while the drink is still properly chilled and fizzy.