"acquired distinction" is correct and usable in written English.
You can use it to refer to a concept or status that someone has achieved through their own work or actions, not something they had naturally or were born with. For example, "After years of hard work and dedication, she had acquired a considerable degree of distinction in her field."
She acquired the distinction of being the "mother" of her church, and people took to calling her Mamma Lizzie.
Almost three months ago, Roache at last acquired the distinction that most of us thought had been his for years, that of the most durable actor in a television soap anywhere in the world.
The Yakama acquired historical distinction in the Yakama Indian Wars (1855 58), an attempt by the tribe to resist U.S. forces intent upon clearing the Washington Territory for prospectors and settlers.
Just by being appointed to lead the New York Philharmonic, a less-well-known American would acquire instant distinction.
Hampton was raised as a Catholic, and thus acquired an uncommon distinction among jazz drummers in having been taught snare-drum rudiments by a Dominican nun.
On Tuesday, nearly 47 years after emigrating from Ireland, Mr. Cohill, 64, acquired the one distinction he had never gotten around to: United States citizen.
Spain acquired the dubious distinction of having the highest concentration — nearly one-fifth — of all the 500-euro bills on the continent.
Seventy years ago the State of South Carolina acquired a dubious distinction: George Junius Stinney was executed at the age of just 14, becoming the youngest person put to death in the United States in the twentieth century.
Under the empire, the toga acquired a special distinction because of its unique and complex method of draping and because, as a note of rank, its wearing was restricted to Roman citizens.
With acquired stenoses, a distinction is made between post-traumatic stenoses, such as the so-called induced stenoses ("kinking"), and surgically created stenoses ("banding") [64].
