There are two secret paths in Fire Island.
The first one is in the grassy area. You can see a chest box on the map and I am sure everyone can manage that.
The second one is really tricky. It is easy to miss this one even with Misto Soup - I know I did. xD
The picture below says all. As you can see, the little island is totally out of the screen. You wouldn't be able to notice it at all if you don't walk onto the sparkle spot on the beach. It's not a straight line of course, but I will leave the fun to you.
The item in the chest box is Silver Tray - Equipment No.60 in Secret Catalog.
Please click here for more info about Adventure Bar Story.
Good luck and have fun!