The phrase "achieve any sort" is correct and usable in written English.
It can be used when discussing the attainment of a particular type or category of something, often in a context where the specifics are not defined.
Example: "Despite their efforts, they were unable to achieve any sort of consensus on the issue."
Alternatives: "attain any kind" or "reach any form".
He understands that his annoyance with this woman's shallowness has to be overcome, if he wants to achieve any sort of relationship with her.
Whether the book will achieve any sort of pop-horror critical mass is hard to say, but Hill seems to know his audience.
"His inability to work with the Legislature has made it difficult for him to achieve any sort of agenda," Mr. Moore said.
Style over substance in music is a dangerous thing, and it's hard to imagine that a fashion band like CSS have got the creative depths to achieve any sort of longevity, which ultimately spoils enjoyment of their music in the now.
In contrast, it's taken years for Google to achieve any sort of cohesion across its own disparate products and projects.
The February G-7 meeting in Boca Raton, Florida did not achieve any sort of coordinated Plaza Accord to strengthen the dollar.
Persistent effort and the willpower to stay the course are the fundamentals for achieving any sort of change.
And there are enormous political obstacles to achieving any sort of agreement between leaders, because it would require nations to give up some of their independence.
And while the wines can differ significantly depending on where along the Loire the grapes are grown and by whom they are tended, only Vouvray has achieved any sort of name recognition beyond the ring of worshipers.
Even at the best times in my career, I was never deluded into thinking I had achieved any sort of rational allocation between my life at work and my life outside.
For those skins who repent, who repudiate their white-power ideals, achieving any sort of atonement is a lengthy journey.
