As Yoshi!-san explains correctly, "by virtue of" is the best option.

△ She won her position by effort of her hard work.
is not terribly wrong, but it sounds a bit unnatural and redundant [くどい]. "her hard work" is a definite amount of work, so
△ She won her position by the effort of her hard work.

is somewhat better, but it is still redundant. "effort" already implies "hard work", so it is almost as if you're writing:
△ She won her position by the effort of her efforts.

"by effort of" is not used very often in everyday English:
◯ She won her position by effort of will.
◯ I learned French vocabulary by effort of reading a lot of books.

ヨシ！さん

ご回答ありがとうございます！知らなきゃ解けないですよね、安心しました〜

Mr.zmic

Thank you for your additional information!
I was able to understand.(*^^*)