"has achieved its purpose" is a correct and usable sentence in written English.
You can use it when you want to refer to a goal or an objective that has been accomplished. For example, "The campaign has achieved its purpose of raising awareness of the issue."
It is hoped that this paper has achieved its purpose to help researchers make better decisions when they develop and validate a WAF test and/or use that test or an existing test for different research purposes.
While I can say that the Sony has achieved its purpose, that purpose is intentionally limited and as such makes it attractive to a rather narrow slice of people.
Hillary Clinton's descent into Atwaterish bark-stripping has achieved its purpose, having helped to insure her victory in the Pennsylvania primary.
This shows that this innovative proposal has achieved its purpose and also ensured patient safety.
However, the study has achieved its purpose in demonstrating that the application of the Lean method; particularly the feasibility of using both the VSM and A3 tools, is an effective mechanism for identifying opportunities for reducing waste, for integrating process steps more tightly, and for standardizing work in the clinical process.
Until recently, defenders of the war often argued that it had achieved its purpose: preventing it from ever again becoming a haven from which al Qaeda could launch attacks against the US.
The call to Hickory Hill had achieved its purpose.
That ogre's twinkle seems to have achieved its purpose.
If my novel contributes to that outcome, Hate will have achieved its purpose.
But the little game show had achieved its purpose at WPIX.
The plaintiff, Katy Johnson, said the suit had achieved its purpose by exposing a Web site that she said degraded women.
