The phrase "a sharp battle over" is correct and usable in written English.
It can be used to describe a fierce or intense conflict or disagreement regarding a specific issue or topic.
Example: "The two political parties engaged in a sharp battle over the proposed healthcare reform."
Alternatives: "a fierce struggle over" or "an intense conflict over".
WASHINGTON — The top two Senate Republicans declared Sunday that they would vote against President Obama's nuclear treaty with Russia as the bipartisan spirit of last week's tax-cut deal devolved into a sharp battle over national security in the waning days of the session.
[Page C2.] Maneuverings in Auction Case The contours of a sharp battle over the fate of A. Alfred Taubman, the former chairman of the auction house Sotheby's, have begun to emerge in courtroom skirmishes and out-of-court maneuverings in the price-fixing case involving Sotheby's and Christie's.
"It was a pretty sharp battle within the agency," said a former senior intelligence official.
France had just defeated Libya in a sharp border conflict over Chad.
At the same time, Mr. Gephardt and other Democrats drew sharp battle lines with the president over the state of the economy, noting the return to federal deficits and the rise in unemployment in the year since Mr. Bush took office.
So, Tate, in positional trouble, put his faith in a sharp tactical battle with 10... g5 10...3 f5.
Over time, and as far-right extremism surged, sharp battle lines between Democrats and Republicans were drawn that left little room for compromise or centrism.
After a hard-fought Republican primary race that featured sharp battles among candidates over health care, abortion, immigration and education, the gender gap yawned most recently in a Washington Post/ABC News poll this week.
A series of sharp battles against the Arabs ensued at Um Rakhum, Gebel Medwa, and Halazin during December and January.
BUSES were being stoned and set on fire in Delhi this week in a sharp escalation of a battle over fuels.
