Put the ¼cup cranberries and the cranberry juice in a small pan. Warm over a medium heat until the berries pop and go soft, squashing them to form a kind of jam texture. Remove from the heat and press through a small sieve to give a syrup/puree. You can do this in advance and in larger quantities to use for a few drinks. You should get around 2tsp from this quantity, enough for 2 drinks. Store extra in the fridge for a couple days.
When ready to make drink, quarter the half lime and place the pieces in the bottom of a glass. Sprinkle over the sugar and add the 5-6 cranberries. Muddle them together so the sugar dissolves, cranberries split and juice comes from the lime (if you don't have a bar tool, then use the pestle from a pestle and mortar, as I do).
Next, top up the glass with ice cubes, pour in 1tsp of the cranberry syrup/puree and the cachaça and stir slightly. Serve immediately.