How about after Dark Link is defeated, the game continues, and Link begins seeking information on this sudden manifestation of evil from him. There could be something that you could get for defeating him, like a weird artifact, which would serve as a gateway into the unknown depths of his very subconscious. You could have to travel back and forth between there and the physical world many times to ultimately uncover the secret. Something else could be that you find out that the 'Dark Link' Link fought earlier was like an empty vessel devoid of any of Dark Link's being, and that he still plagued Link's mind. Link would eventually find the true Dark Link, and the real final battle would commence.

Does that sound any good?