For anyone who are stuck in the 2nd island and don't know how to get to the 3rd island :
1. In the big city, at the big fountain area, a character want a fruity ice cream.
2. In order to make it, you'll need a blue ice fruit, that you can find in the forest, south of the city.
3. Cut it together with any other fruits and you'll get it!
4. By finishing that quest, you unlock a new party member and the ability to create equipements/weapons, upgrade them, and create consomable items. You can also talk to the naked man to sell your cloths, with interest rate depending on how smelly it is (you can potentialy exceed 3x the original price!).
5. Then, finish the desert dungeon in the west and you'll be able to go to the next island by going to the village at the bottom south.
PS : I can't seem to see the new character, despite the option existing in the data menu... Is it just me?
EDIT : male's smell actually significantly lower the cloth's value (make sense, I guess). It seems to increase a lot slower than girl's smell, so you can probably remove it without too much damage if you wash her carefully.