"strove hard" is a correct and usable phrase in written English.
It is used to emphasize someone's effort in attempting to do something. For example, "John strove hard to finish the project on time."
Auction houses strove hard to increase their part of the cake and only the fittest survived.
Entrepreneurs strove hard but did not yet develop a staple industry.
She strove hard in the face of poverty to provide a formal education for her four daughters and one son, although she herself was uneducated.
("The papers strove hard to portray [her] as an evil temptress … but by 1927, Ruth Snyder was 36 years old, plump, haggard and worn").
For this reason alone, Washington, a decade ago, strove hard to keep Israel on the sidelines as it prepared for Desert Storm.
Slipped in alongside reproductions of Bacon's art, they at first seem a jarring intrusion – Bacon strove hard to avoid what he called "the trap of illustration".
Some at Annie Wright strove harder for grades than others, but this seemed to be a matter of temperament rather than need.
A1 Mr. Gore, campaigning by riverboat on the Mississippi, said some people strove harder and less successfully than others and that he was seeking to be their champion.
The team lost only two matches during the tour, with Wisden saying, "No travelling team ever strove harder for victory or more completely subordinated all personal considerations to the prime object of winning matches.
Mr Koons strives hard to create convincing illusions.
Mrs. Murillo strives hard not to surrender her hope.
