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The phrase "achieved a high" is correct and usable in written English.
It can be used when discussing reaching a significant level or standard in a particular context, such as performance, score, or achievement.
Example: "The student achieved a high score on the final exam, demonstrating her understanding of the material."
Alternatives: "reached a high" or "attained a high".
Exact(60)
The Brundtland Commission achieved a high level of global consensus through its trademark public hearings.
Only 54 State Department employees had achieved a high level of fluency in Arabic.
There he established an ashram and achieved a high reputation as a sage.
Mr. Hersch's own "Endless Stars" achieved a high level of reflective jazz impressionism without lapsing into twiddling, new-age vagueness.
With all this criminal law, we ought to have achieved a high level of corporate honesty by now.
He says Latvia has achieved a high degree of convergence with the eurozone (see 11.31am for details).
Using a style that is remarkably free of artifice, the authors achieved a high point in detail, clarity and coherence.
Royal sculptures, particularly of Sesostris III and Amenemhet III, achieved a high degree of realism, even of portraiture.
That approach achieved a high overall accuracy of 100%%.
We tested the proposed method on our patient database and achieved a high classification accuracy.
All crops combined in one analysis have achieved a high WIA of 0.92.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com