The Island Heart can be obtained by completing the purple quest from the island.
To unlock the quest you have to do a purple quest in Stern (Arthetine) which will lead you to Bikini Island for completing it.
2.1. Quest Details
Starting in Stern you have to accept the purple quest seen in the picture below.
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The quest will lead you to Cruise Ship Paradise Peyto where you have to take 3 photos and removing painist at work, followed with buying 3 drinks from a barkeeper.
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After completing the quest, head back to Bikini Island where you can now accept the purple quest which will give you the Island Heart as a reward.
