Do I need Magic Wisdom to defeat the Spectre in Pathfinder ACG?
If there is a way to augment a Wisdom check with the Magic trait, I'm unaware of it except with using Divine spells or items.

Weapons and/or spells with the Magic trait work for the Combat check.

Either way, you cannot use a straight Wisdom (or straight Divine) check to defeat a Spectre; as it's Incorporeal, it must be defeated by magical means.