Add all the ingredients to a high-speed blender in the order listed and blend until smooth.
Taste and adjust for sweetness, add more sugar syrup if needed.
Refrigerate 4 martini glasses.
Pour into 4 martini glasses over ice and garnish as desired. Serve cold.
Method using a food processor:
Puree mango and pineapple in a food processor.
Add the puree to a jar and add Bacardi, sugar syrup, pineapple juice, and 1/2 cup water. Stir and refrigerate until chilled. Refrigerate 4 martini glasses.
Add a few ice cubes to the glasses. Stir the cocktail and pour into glasses. Serve.