This is a TWO controllers method to be used in split screen.
It's highly recommended to do this achievement after clearing ALL islands form the greed (bomb all five caves). First you don't miss the several days you need for this and second you need two empty islands to sail.
For the first controller
it'll be easier to use the Unicorn (Kirin on Shogun mode), that can picked up at Island 5. Using this method, every time you have to wait for the boat eat some grass to make coins, so you'll have enough money to afford the bell and the trips.
As stated above you'll need a second controller, after your main one is in the game press
at the second to enter the game, choose to enter split screen. I recommend to do the entire game in split screen, it requires a lot more management but becomes a lot more easier and faster.
Choose two islands, number 1 and another. The best second island to choose is one that the docks is most near the bell, that's because every time you arrive at an island your boat is going to sail from the docks to the bell. For me was Islands 1 and 3.
Next, at this islands build the 3rd level lighthouse (last one), so your boat don't crash when you arrive. The best thing to do is build these as you clear the island and before move to the next during your normal playthrough.
Now go to Island 1, build the boat (if you didn't) and ring the bell. Go with both mounts over the boat and with the first controller pay the coins do sail way to your chosen second island. Arriving there do the same thing and go back to Island 1. Repeat, repeat and repeat until achievement is unlocked. For me it took 47 in game days, this because I did the entire game in split screen.
Very important: you have to ring the bell and
WAIT for the 3 builders to jump in the boat before sailing way. They are the one that push the boat from the dock to the bell when you arrive at an island. If you don't bring them you'll have to wait a LOT of time to builders from the town.