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The phrase "achievement was based" is correct and usable in written English.
It can be used when discussing the foundation or criteria upon which an achievement was established or evaluated.
Example: "Her achievement was based on years of hard work and dedication to her craft."
Alternatives: "success was founded on" or "accomplishment relied on".
Exact(8)
Mahoney's achievement was based on media relations.
Her achievement was based, instead, on an extraordinary intuition of the musicality of language.
Its achievement was based on comfortable, roomy garments -- silhouettes were not the point -- that let the fabrics rule.
This achievement was based on the development of centralized patterns of political control and the growth of a type of authoritarianism involving the rule of a military elite.
The research was based on one group, pretest-posttest experimental research design in which analysis of the target group's achievement was based on t-test using SPSS/PC+ program.
Reported achievement was based on fairly simple statistics and item response theory and related methods were relative new-comers and not often used in educational research.
Similar(52)
In the real world, that is outside of Washington, D.C., compensation and achievement are based on goals defined and achieved.
A new achievement is based on a commodity NVIDIA Quadro K5000 graphic card and Compute Unified Device Architecture (CUDA) C language.
As a Taiwan citizen, I feel honored by Mr. Friedman's column, not just because he says Taiwan is his favorite country aside from his own, but because he likes how Taiwan's economic achievement is based on education.
And at the centre of it all is the WNO Chorus, delivering Schoenberg's ferociously tricky writing as if they have been doing it all their lives; together with the orchestra they provide the foundation on which this unmissable musical achievement is based.
Their achievement is based on a geometric concept known as the Berry phase and is implemented through entirely optical means within a single electronic spin in diamond.
More suggestions(16)
attainment was based
advancement was based
implementation was based
resulted was based
achievement was limited
achievement was estimated
achievement was measured
achievement was broadcast
achievement was expected
achievement was tarnished
achievement was considered
achievement was reported
achievement was reduced
achievement was bracketed
completion was based
victory was based
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com