Dream of the Windfish
Ganon had been destroyed, but the people of Hyrule didn't trust him to stay that way. From Ganon's ashes came suspicion and fright, the the people of Hyrule were always preparing for him to return. Rumor had it that if the blood of the one who had slain Ganon was sprinkled over his ashes, Ganon would be able to return to life. Link, in an attempt to be ready should this event ever occur, left Hyrule on a journey of enlightenment. He saw many new lands and met many new people. Finally confident in his abilities, he set off across the sea en route to Hyrule. But the sea had something else in mind. A sudden storm shook Link from his raft and plunged him into the water. He tried desperately to swim, but the waves were too powerful. Link began to black out...
...and awoke in a nice warm bed. A girl named Marin explained to Link that she had found him washed up on the shores of Koholint Island. She had since tended to him in hopes that he would awaken. Link, after retrieving his sword from the beach, set out to explore the island. He came across an owl, vaguely reminiscent of Kaepora Gaebora, that explained the nature of the island to him. Apparently a giant egg that sat at the peak of the island housed the sleeping Windfish, and the entire island existed solely in the Windfish's dream. As such, the only way Link could leave was by waking it up.
The owl sent Link after the Siren's Musical Instruments, which when brought together could wake the Windfish. Link traveled all over the island in search of the instruments, defeating various nightmares for possession of them. Upon collecting all of the instruments, Link found himself torn. If he woke the Windfish, this entire would would disappear - including Marin, who Link had grown quite close to. Link eventually made his decision, and opted not to live in a dream world. He played the instruments, and found himself floating on the remains of his raft out at sea. The Windfish, a massive winged beast, flew off into the distance.
Link decided against returning to Hyrule. Perhaps effected by the choice he had to make regarding his latest adventure, he settled down in a distant land and lived a normal life. However, it was not meant to be.
Chapter 6 Notes
Facts for Chapter 6 were taken from Link's Awakening.
These last three chapters are fairly short, at least in comparison to the previous 5. But that's what you get with Game Boy and NES titles. There's some story at the beginning, and some story at the end, but the middle is pretty barren.
So why are elements from Ocarina of Time present in Link's Awakening? Namely Marin, who is very reminiscent of Malon, and the owl? Well, I think it's safe to assume that the Windfish was a very ancient creature. Most mythical beasts are. As such, it could have easily been around during the events of OOT, and witnessed many of them. For that reason, images from its past could easily pop up in its dreams. And that's something that people need to remember. LA doesn't take place in Link's dreams, so it doesn't have to be the same Link as the one in OOT.