The phrase 'make great accomplishments' is correct and usable in written English.
For example, you could say: "John has worked hard to make great accomplishments in his career."
When they make a great accomplishment, compliment them.
The subversiveness inherent in Austen's accomplishment — a woman making great, lasting art by describing little, fleeting lives — has been overshadowed by the pleasures she offers.
Because despite our national mythology of "the self made man," no great accomplishment has ever been achieved alone.
He called on all sides to compromise; the day before, he had visited the tiny prison cell on Robben Island where Nelson Mandela, one of whose great accomplishments was making sure that his country's second post-revolution election succeeded, was held for eighteen years).
In painting, culturally-codified picture making was revitalized with great accomplishment by Gerhardt Richter, Eric Fischl, John Currin, Jenny Saville, Lisa Yuskavage, Shazi Sikander, and Dexter Dalwood.
Making religious freedom possible for the Shiites was one of the great accomplishments of the war, as administration officials rightly claim.
Pepys had two great accomplishments.
With great accomplishments come a lot of questions.
It won't be easy, but great accomplishments never are.
The shuttle program had great accomplishments.
