"achieve high levels of" is correct and usable in written English.
You could use it to express the idea that someone is working hard to meet a certain goal, or they have accomplished something noteworthy. Example sentence: He has worked hard to achieve high levels of success in his career.
Current levels of resource and energy consumption indicate that not all of the world can achieve high levels of development.
Nor that popular works cannot achieve high levels of artistic excellence.
"Europe and Asia require their students to take numerous language courses and achieve high levels of proficiency.
A number of countries have already managed to achieve high levels of human development with very low levels of consumption.
But it states that EU countries "face different starting points in the challenge to achieve high levels of both productivity and employment".
According to a report commissioned by the Forestry Commission (pdf), people with access to large, attractive open spaces are 50% more likely to achieve high levels of walking.
And, conversely, where the direct customer contact is high, the less the potential that exists to achieve high levels of efficiency.
A nation's standard of living depends on the capacity of its companies to achieve high levels of productivity and to increase productivity over time.
Study after study has shown that teams are more creative and productive when they can achieve high levels of participation, cooperation, and collaboration among members.
The various parts of the design were highly interdependent, which Apollo's designers believed was necessary to achieve high levels of performance in the final product.
Societies that achieve high levels of health and longevity for most, while the poor and marginalized die young, do not comport with social justice.
