Zelda II: The Adventure of Link/Fairy Feet Encounter Skip
It's possible to glitch the game into putting Link on the wrong overworld tile, when leaving the side scroll, to the overworld, in a place with a two-sided tile. Examples of this are bridges and forced encounters.
You move link one pixel too far to the left/right, past the edge pixel that sends link back to the overworld. This is done most easily by casting fairy, and doing one frame taps toward the edge until the fairy disappears. Then you move BACK in the opposite direction, and link lands in the overworld on the opposite side he's supposed to land on.
It is doable without fairy, though apparently you need the right subpixel for Link, and fairy gives you them.