Stopban||Ngo Bao Anh

"Cat's grace" is when a person moves so smoothly, easily and naturally that the movements resemble those of a cat.
For example:
walks softly, without sudden steps;
keeps the body relaxed and confident;
movements of arms and legs are smooth;
easily changes direction and position;
can move almost silently;
even when just turning or sitting down, it looks very smooth;
The movements are not necessarily slow - the cat can move abruptly, but still very coordinated.

For example, a person may appear "cat-like" if he or she has:
the look or shape of the eyes resembles a cat's;
movements are smooth and careful;
he approaches quietly or walks almost silently;
loves his own space and doesn't always like being touched;
can be very affectionate, but only when he wants to be;
sometimes abruptly changes mood or interest in something;
there is a habit of stretching, curling up, or getting comfortable in one place.

The phrase "she has a cat-like grace" rather means: "she moves very smoothly, flexibly and confidently, with good coordination."