The phrase "achieves a level" is correct and usable in written English.
It can be used when discussing reaching a certain standard, degree, or stage in various contexts, such as performance, skill, or quality.
Example: "The athlete consistently trains hard and achieves a level of performance that sets her apart from her competitors."
Alternatives: "reaches a standard" or "attains a degree".
In his book Absent Minds: Intellectuals in Britain (Oxford, 2006), Collini goes to the other extreme, arguing that a public intellectual is someone who first achieves a level of creative or scholarly achievement and then uses available media to engage with the broader concerns of wider publics.
Whatever the case, Ms. Goodman achieves a level of expression that is always visually stimulating.
She still achieves a level of success here, even though it is the least effective work in the exhibition, because she does not waver from her original intent.
So if a student achieves a level 5 at primary school, by hook or by crook (revision, endless prep, primary schools flogging themselves to the bone) then the data says they'll achieve a grade A at GCSE.
Williams invariably achieves a level of craftsmanship that no other living Hollywood composer can match; his fundamental skill is equally evident in his sizable catalogue of concert-hall scores.
For critical, real-time applications, scoped memory management in Real-Time Specification for Java (RTSJ) achieves a level of predictability not found in applications that use garbage collection techniques.
One cannot achieve "A" level results with a "B" level team or a team that is not fully staffed.
He achieved a level of fame which was extraordinary.
"Every third grader," she said, "can achieve a Level 2 or Level 3".
"He achieved a level of responsibility that he didn't before.
Learning to work hard, get tougher, achieve a level of responsibility commensurate with his talent.
