Its elemental weakness and resistance change from battle to battle. It starts the fight by casting Doom, and if no one is doomed on its turn, it may cast Death. It is one of the only enemies from which Kimahri can learn the Doom Ronso Rage.
It drops weapons with Strength+5% and Strength+10%, and armor with Magic Def+10% and No Encounters.
Using an aeon when fighting against one or multiple Wraiths is a wise choice as aeons are immune to both Doom and Death. An aeon like Shiva or Ifrit is a good choice, since they can heal themselves. Delay Attacks can also be used and the party can win the fight without the Wraith even getting a turn.