"groundbreaking attempts" is correct and usable in written English.
You can use it when referring to efforts towards something innovative, important, or revolutionary. For example: "The scientist's groundbreaking attempts to find a cure for cancer have been inspiring."
In August this year, the Reproducibility Project - a groundbreaking attempt to systematically assess the reliability of published psychological research findings - delivered a grim result.
Jonathan Jones Courtauld Gallery, London, 17 September 17 January Groundbreaking attempt to place pop art in its global context or another rehash of familiar names and images?
Written by Heike Görtemaker and published just last week, "Eva Braun: Life with Hitler" is a groundbreaking attempt to dismantle the prevailing ideas about the woman who was Hitler's longtime companion — and, for forty hours, his wife.
When researchers decided to survey attitudes, values and the impact of Sept. 11 among 1,000 Arab-Americans in the Detroit area, they saw their study as a groundbreaking attempt to accurately portray a community that felt stereotyped and under siege.
More than a million people in the UK are so poor they cannot afford to eat properly, keep clean or stay warm and dry, according to a groundbreaking attempt to measure the scale of destitution in Britain.
So many boards use sex to rise above the clutter that the latest groundbreaking attempt, in which healthy young men and women seem to have literally and completely leapt out of their color-coordinated outfits, barely draws a glance.
From EMI's point of view, the system is a groundbreaking attempt to institutionalize a third legitimate music format, the digital download, in conjunction with the CD and cassette.
Karl Mathiesen (@KarlMathiesen) Robert May's groundbreaking 1988 attempt to estimate the #numberofspecies using measurements such as size.
There are scores of artworks in "Art AIDS America Chicago," the new and groundbreaking exhibition that attempts to survey AIDS-related art and make a case for its lasting influence on the art world.
In fact, Mr. Steinberg's reputation was built largely through his groundbreaking but failed attempt to take over Chemical Bank in 1969, a precursor to 80's-style corporate raids.
