The Specter is weak to Holy. It shrugs off a long run of debilitations: Blighted, Sleep, Caught Fire, Drenched, Tarred, Frostbite, Unconscious, Petrification and Silence have no effect on it. It drops Eldricite and Hunk of Rift Crystal. In a fight you can also pilfer Putrid Gold Tooth, Scrap Iron, Eldricite, Fell-Lord's Bone, Black Crystal, Giant Hunk of Rift Crystal or Wakestone from it.
The map has 3 Specter spots, and they sit around the Precipitous Catacombs, so head there if you want to face one in the regular world. The Unmoored World has 14 spots. Vernworth has the most with 3, then Moonswax Bridge and Nameless Village with 2 each, and the Arboreal Ruins and the Bridge of Theodracus the Second with 1 each.
Eldricite
Hunk of Rift Crystal
Putrid Gold Tooth
Scrap Iron
Fell-Lord's Bone
Black Crystal
Giant Hunk of Rift Crystal
Wakestone