Six soldiers total defend the empress: three killed silently outside, three still in the throne room.
There are only three guards outside the small Prism Kingdom castle. Carl and Donut sneak up on them and kill them before they even know anyone is there—though Carl notes the Death Chime Flaw means any attentive officer would have been warned by the notification.
Nobody else comes charging out the door. Inside, the Hunter Seeker Automatons find three more guards in the Throne Room with Empress D'Nadia. Six soldiers are the whole of the empress's protection, the consequence of the Quarantine and her having spent every penny reaching the plains.
Ordinary soldiers of the Prism, few in number, three posted outside and three inside the throne room.
The empress's entire bodyguard, half of them killed before the raid even begins.