Beat 5 islands in One Playthrough.
You can not pick the same island right after you beat it, but you can -
Pick island 1 then 2 then 1.
Counts as 3 lands ^
Pick island 1,2,3,4, and then 5.
Counts as 5 lands ^
Achievement does not pop until you land on your 6th island.
Do not lose your crown or it will count your new king/queen as a new reign.
Goodluck!