Place fish in a non-reactive bowl. Add lime juice, club soda, sugar, salt, pepper and rum. Toss to coat evenly. Store under refrigeration for approximately 45 minutes to allow the citrus to begin cooking the fish. Stir every 15 minutes. Add the remaining ingredients to order. Serve in individual cups and garnish appropriately.
Garnish with additional mint, lime zest, lime wedges and tortilla or plantain chips.