(Like I said yesterday, this route presumes doing the bat caves and the astrolabe puzzles on the same trip is faster than doing the Half Moon Reef and beacon fetching on the same trip.)
Okay, so you get Johnny's glowsticks for the endgame challenge, at the same time you get the bat battery. You then head to the bat caves. Here, you solve the bat cave puzzles. Once that's done, climb right up the mountain and put the perch/astrolabe in place. You find the two islands, to unlock their puzzles.
I'm pretty sure there isn't a timing difference, in terms of which island you visit first. You'll do both islands on the same boating trip, so no matter which one you go to first, your route ends up being a triangle.
On Half Moon Reef, you go to the bottom/left area for a shell. Use the shell to lure the octopus out of its cave, then solve the puzzle the octopus hides. On Dove Island, you see the puzzle and call George. George has to play a game with the monkeys, so she can get the number Nancy needs. Nancy uses that number to solve the puzzle.
Back on the island, Nancy has to use the metal detector on shark beach, to find the metal puzzle parts. When she solves that puzzle, she gets a dial. Then she goes to Blue Hole and solves the pulley puzzle for the final dial. She can do this on an earlier trip to Blue Hole, if I'm not mistaken, but it doesn't make a difference timewise. You'll still have to go to Blue Hole, after getting all the dials.
You dive at Blue Hole, solve the maze puzzle, solve the dials puzzle and solve the hourglass puzzle. Nancy finds the treasure at this point. You return to George, then go to Johnny for a scene. You solve the final key puzzle, and you're done.