The ingredient list includes Cachaca, a Brazilian rum-like liqueur (which is what I use). But you can use rum if you don't have Cachaca on hand. It might not have the exact same flavor as Cachaca, but it'll be rather close.
Muddle a few slices of lime in a cocktail shaker. Add Cachaca (or rum), pomegranate juice, sugar, and ice, and shake about 10 times. Pour into a chilled martini glass, and garnish with a slice of lime.