Palace Guards are basically another variant of Theron Guards, and are only seen in the Queen's palace in the Nexus. It seems only the highest-ranking Locust are accepted as Palace Guards.
The shape of their armor can confuse you with the location of their head, making it difficult to achieve headshots. They wear silver armor with only two small spots on their helmet in which they can see through, and use nearly the same arsenal as Theron Guards. Unfortunately Palace Guards are not available in multiplayer.
To take these guys down, I suggest you use the Lancer and just wail on them. If possible, use the Gnasher Shotgun melee then follow up with a blast to the face. Sniper rifles are also very effective as headshots, though hard to achieve on these enemies, are still very effective. Beware though, as they use Torque Bows.