So there are four upgrades for Nephilim's Respite as follows:
Bonelands - Hulking Carcass - Upon entering the Bonelands, continue forward from Vulgrim’s location through the swamp. Against the far wall, behind a large tree you’ll see an Elite Undead Angel. Kill him and then loot the corpse he was guarding for an Invigoration Core.
Depths - Sunken Tracks - After leaving the Vulgrim point and reaching the room with the train puzzle, kill the pair of Harvester Spiders. Once the area is clear, look for a corpse to loot on the far subway platform from the entry point to find an Invigoration Core.
Hollows - Antechamber - This Invigoration Core is found in the same room as the Vulgrim point. It is located at the base of a large statue at the top of a small flight of stairs that a small group of Skeletons is worshiping.
Scar - Drilling Annex - When you reach the large wooden structure suspended over the pit of magma, look for a Force Crystal wall we can jump to behind and to the left of the elevator platform. On the small outpost platform at the end of this Force crystal path is an Elite Phantom Guard, Phantom Guard and a Phantom Spearman. Kill the Elite for a Piece of Adamantine, loot the corpse on the lower level for a Large Lurcher Cache and the top floor for an Invigoration Core.