Killed the shade of the Priest-king yesterday 4 times. Got 3x Derketos Voice and 1xSets-tongue (daggers).
Little summary:
Gate Guardian can drop (but can also drop NOTHING special):
- https://conanexiles.gamepedia.com/Axe_of_the_Gate_Guardian
- https://conanexiles.gamepedia.com/Fragment_of_Power
- https://conanexiles.gamepedia.com/Legendary_Armor_Patch_Kit (can be more than 1. Max I got was 3)
Warmaker shade can drop (1 fix drop):
- https://conanexiles.gamepedia.com/Nortis
- https://conanexiles.gamepedia.com/Balias
- https://conanexiles.gamepedia.com/Ranissan
- https://conanexiles.gamepedia.com/Mordlun
Priest King shade can drop (1 fix drop):
- https://conanexiles.gamepedia.com/Ymir's_Targe
- https://conanexiles.gamepedia.com/Set's_Tongue
- https://conanexiles.gamepedia.com/Derketo's_Voice
- https://conanexiles.gamepedia.com/Jhebbal_Sag's_Prowl
- https://conanexiles.gamepedia.com/Crom's_Hammer
- https://conanexiles.gamepedia.com/Mitra's_Justice
- https://conanexiles.gamepedia.com/Yog's_Touch
I didnt got Mitra or Yog weapon from Priest-king tough. Every other weapon I got at least 1 time.
Archivist shade can drop this buffs (1 fix):
- Blood-stained Nails
- Denizens of the Dark Well
- Prince of the Black shores
- Prophecy of the Borne Witch
- The Daughter of Ymir
- The Mastodont’s Tower
-
Time of the Scaled Lizard
(just copied this from the wiki page)
He-Who-Walks-Below can drop (may drop nothing):
- https://conanexiles.gamepedia.com/Annihilator
- https://conanexiles.gamepedia.com/World_Breaker (didnt got it to this day)
Arena Champion can drop:
[nothing special - just armor scraps so far]
In the area where she is, there is the stele to learn her armor. On the other side is a chest, where you have legendary armor patch kit or legendary weapon repair kit!
Champion of the Warmaker can drop (always armor scraps - but besides that he may drop nothing):
- https://conanexiles.gamepedia.com/Carnage
- https://conanexiles.gamepedia.com/Destroyer (didnt got it)
He-Who-Walks-Below is really frustrating… Already have 3 Annihilators and zero World-breaker… Killed him yesterday 4 times and he didnt drop ANYTHING at all… 
Thx @Gnadolin and @Born2bAlive
And maybe I am missing sth? Can the Gate-Guardian drop sth else?