With a knife, shave off the stem end of the watermelon, just enough so that it sits flat. Cut the top off the watermelon, about 3 inches down. Scoop out half of the watermelon with a melon baller and set aside.
Scoop out remaining watermelon, leaving the rind-bowl. This will be your punch bowl. Transfer scooped out melon (not the melon balls) to a blender and puree; may be done in batches. Push watermelon puree through a strainer to remove pulp and any seeds. Return watermelon water to the watermelon punch bowl. Stir in tequila, triple sec, and melon balls. Top off with lemon-lime soda. Serve cold over ice.