You probably won't be able to get all of Caribbean without engaging the other nations running in the colony race. So create the colony nation of Havana and put colonies on each island or conquer the other nations colonies here and you will earn this. Highly recommend beginning of one of the big western colony nations for this one.
don't forget to check the map and toggle "Region" to see what count as Caribbean. It will state so on each province info, if you are unsure what counts and what not.