A Link to the PastDesert of Mystery, being perched on top of ledges or cacti. When Link draws near, the Vulture begins to fly and circle around him. If Link does not move at all, the Vulture never tries to attack him and just continuously flies around him in a circle. In fact, Link must make an effort by moving directly in the Vulture's path in order to get harmed at all.
A Vulture alone is not much of a threat for Link. The other desert obstacles in combination with the bird can be damaging. When attacking a Vulture, Link needs to move around and can potentially run into the damaging cacti, the land mines, or the enemy Geldman.
Link can defeat a Vulture with six slashes from his Fighter's Sword. A safer way to defeat the enemy is by hitting it six times with the Boomerang. Later in the quest as Link acquires more powerful weapons, a wide variety of them can be used to defeat the Vultures.