ISLANDERS: Console Edition (UP)

This is cumulative over all your games, so it's not explore 10 islands in 1 game, it's explore 10 islands over the course of many games. For me this unlocked during my 3rd game (was getting to the 4th island in the other 2 games). There's really no need to farm it as it will unlock naturally as you play.

You unlock new islands during the game based on score, you can see the progress to unlocked the island in the bottom right, and once the new island is unlocked you can press Y to travel to the new island.