The phrase "achieving the ability to" is correct and usable in written English.
You can use it when discussing the process of gaining a specific skill or capability.
Example: "She is focused on achieving the ability to communicate effectively in multiple languages."
Alternatives: "gaining the capacity to" or "developing the skill to".
For one, the prospect of Iran's achieving the ability to make a nuclear bomb has cooled European enthusiasm for investing.
With an almost professorial air, Mr. Netanyahu held up a diagram of a bomb with a fuse to show the Israeli view of Iran's progress in achieving the ability to make a nuclear weapon.
The bigger question is whether Mr. Rouhani is in the position to make concessions on a nuclear program that Tehran insists is for peaceful purposes and that the United States suspects is aimed at achieving the ability to produce nuclear weapons.
American and European Union sanctions on Iran are aimed largely at pressing the country to halt its uranium enrichment activities, which the Iranians say are peaceful but which Western governments suspect are a cover for achieving the ability to make nuclear weapons.
Recently, one of the most important scientific issues for a better future life for humanity is achieving the ability to intelligently harvest, store, and utilize energy with good efficiency because we are facing critical environmental pollution and exhaustion of energy resources.
Achieving the ability to work with large models is primarily a technical challenge.
The Western countries and Israel suspect it is meant to achieve the ability to make nuclear weapons.
Within a few generations, Babylonian astronomers had achieved the ability to predict the behaviour of the Moon and the planets.
It is from this mathematics of learning and big data that a machine can achieve the ability to generate 'intelligent' decisions.
Skills achieved; the ability to tell the difference between a rock and a clump of mud and throwing stones really far.
Iran contends the enrichment is for peaceful purposes, but much of the world suspects it is meant to achieve the ability to make atomic weapons.
