This is not story related as mentioned above. You can finish the story without activating a single Pirate Lookout, although some of them are very hard to miss.
The Pirate Lookouts are located in the following locations:
Candy Kingdom - 1
Evil Forest - 2
Fire Kingdom - 1
Firebreak Island - 1
The video below is part 1 of a full achievement guide with timestamps for each pirate lookout: