As the parent of a Straight ‘A’ gifted child I can say for a fact Hard Work is the most important factor.
As a former straight A gifted child, I can say that you're wrong. Maybe hard work is the most important factor for your daughter, but you can't extrapolate from her to every successful student.
The only year in my education in which I worked hard was my first year at university, partly because I didn't know how good I was relative to my peers and wanted to compete, partly because a quarter of my course was material which I did actually need to work at, and partly because my one-on-one for that material was with someone who really pushed me. When I finished in the top three and won a scholarship, I didn't feel the need to prove myself in the second and third years, and I had more freedom to choose courses which I found easy. The most important factors for my academic success were intuition, a memory which was good at retaining the things that matters for the subjects I chose, and curiosity.
Just to be completely clear: I'm not knocking hard work. The person who finished first in my course in the second year was a friend whom I met up with once or twice a week to explain the things they hadn't understood in lectures. I think they worked quite hard, and maybe I could have finished first if I'd worked harder. But I preferred to spend about twenty hours a week working and have lots of time to participate in various student societies, because university is about more than grades. (I still got first class honours, so I didn't judge it too badly!)