This type of Guardian does battle air-borne, which can make this particular enemy difficult to defeat, as Link's offensive options are narrowed down. They fly around an assigned path, shining a spotlight on the ground below. If Link enters this spotlight, the Skywatcher will activate, and, as with other Guardians, will begin charging its laser beam.
Like Beamos that have appeared in modern Zelda games including Skyward Sword, Link is able to defeat this creature by shooting its eye with the use of a Bow and Arrow. Ancient Arrows in particular are very powerful against these enemies, since one successful shot to the eye will take it down instantly.
Other strategies that can be used to defeat Guardians include utilizing the Perfect Guard ability, where Link can deflect the Guardian's laser with his shield at the right moment to take down the enemy upon three successful deflects. Link should be wary though, since if he fails to Perfect Guard, the laser may still hit him and cause significant damage.