HOW TO EARN 7 ACHIEVEMENTS BY ONLY DEFEATING THE GREED IN 1 ISLAND
This is a solution for :
So, what happened to me was that I was on my first reign (didn't die or lose the crown), and I came back to Island 1 to bomb the cave (my first).
When you light the bomb in the cave, you have to escape before it explodes, I didn't escape in time, I died, so when the game saved and prompted me some message with in the background the exterior of the cave, I earned
then I quit.
I reloaded my save, and earned
and so on.
Each time I loaded my save, the counter of islands freed went up by one, when I got to 5, I also earned
because the game thought that, even if I died, this was my fifth island defeated, so it gave me this achievement.
I even did this quit/reload one more time to earn
even if this is a DLC achievement (which I have not), I got the corresponding achievement.