The phrase "a hard time improving" is correct and usable in written English.
It can be used when discussing difficulties or challenges someone is facing in making progress or enhancing a skill or situation.
Example: "Despite his efforts, he is having a hard time improving his performance in the competition."
Alternatives: "struggling to improve" or "finding it difficult to improve."
Pep Guardiola will have a hard time improving this staggering side.
If Aqib Talib can cover AJ Green as effectively as he did Julio Jones, the Bengals will have a hard time improving in that department.
Kevin Millar entered this homestand as one of the primary culprits for the Red Sox' woes, and the team knew it would have a hard time improving without more production from Millar, its slumping first baseman.
As a result, the emerging business owners had a hard time improving their sales.
But experts say the country has had a harder time improving quality.
The lack of a salary cap hurts smaller-market teams, and the bizarre (to me, anyway) exclusion of foreign players from the draft means bad teams have a harder time improving through getting their hands on young, franchise-changing athletes.
Though the franchise is right to upgrade skeletally by sprucing up existing restaurants and reducing prices, it is having a much harder time improving the blood and guts of the operation: its massive and far-flung staff.
"G.M.'s a lot better company than it used to be, but it's having a hard time keeping up with meaningfully improving competitors," said John Casesa, an auto analyst for Merrill Lynch.
Medicare allows you to go to almost any private doctor or hospital you like, and has been enormously popular among its beneficiaries, but it costs about a third more per person and has had a hard time getting doctors and hospitals to improve the quality and safety of their care.
7/10 Mike Ross Rosss had a bit of a hard time against Rhys Gill in the first half but improved as the game went on.
Don't worry if you have a hard time learning to speak with a New Jersey accent, it'll all be improved if you just practice well enough.
