"reach a high level" is correct and usable in written English.
You can use it to describe when someone has achieved a high level of expertise or skill in something. For example, you could say "Daisy worked hard to reach a high level in her karate classes."
"You could see last year that Tottenham were a very young team that could reach a high level once they added a little experience.
My mother had also overcome many professional barriers to reach a high level in her field, in a country different from the one she grew up in.
The New Yorker, January 30 , 1978P. 32 Young men studying for the priesthood try to reach a high level of holiness during and after the annual retreat period.
By J. F. Powers The New Yorker, January 30 , 1978P. 32 Young men studying for the priesthood try to reach a high level of holiness during and after the annual retreat period.
Astronomy was the first natural science to reach a high level of sophistication and predictive ability, which it achieved already in the second half of the 1st millennium bce.
Where Sorkin writes motives for Zuckerberg, Fincher uses his camera to go beyond the script to reach a high level of the art of portraiture — mainly done with fixed-frame shots that look long and hard and deep at the characters.
"This will help us reach a higher level".
"They don't want to master a skill just to reach a higher level.
"It takes you into a space where you reach a higher level within yourself, it brings an awareness".
When they reach a higher level, such as a barista maestro, they go for more formal training sessions.
But whenever it seems about to reach a higher level, it slides back into sincere, prettily photographed blandness.
