The most well trained soldiers available, but even they can't be expected to win a fight against a Remnant without preparation.
The royal guards are equipped with the finest of plate armour and have access to all maner of weapons, but traditionally swords and halberds are the weapons of choice.
The royal guard is a purely defensive organisation in service of the king. Therefor they don't need to know any offensive tactics. The defense is furthermore rather specialised in that they are protecting a person, not a location.
The royal guard are expected to train about four hours per day, most of it physical. Then they are expected to be on duty for about six hours, as well as an hour or two to maintain their gear.
Those who excel in the regular army have a chance to be selected to be part of the royal guards. The selection process begins with an officer of the army recommending a soldier to the royal guards. Should they have a spot open they will allow the soldier to prove themselves in a test. This test is made to find the limits of the participants, both mentally and physically.
A common limit is their knowledge about royal etiquett, but that, as well as other training related to being in the precense of the king, is expected to be lacking.
If acepted the soldier is then put under the care of a small group of guards who make sure that the soldier is trained to a higher standard. Properly training someone is seen as a mark of pride among the royal guard.