Valerian moved through the palace corridors at a calm pace, he was walking without any sound. The moment he put down his feet on the ground, he would slide in slightly to cancel the noise as much as he could. This was a method that Fallax taught him to maintain stealth. Fortuna was moving ahead of him at a distance of a few ten meters.
They did this on Fortuna's insistence. She told Valerian that she can now control her dragon aura and remain undetected. The other thing that she had to her advantage was the shape she had taken. The cat of the princess did not seem to be a magical beast and thus, the secret forces hiding inside the palace will not mind her, and Fortuna will take them down silently with her keen senses.