"make a final effort" is correct and can be used in written English.
For example, you could use it at the end of a letter: I hope this letter has persuaded you to our point of view; if not, we will make one final effort to change your mind.
Judith's penchant for storytelling has baffled Andrew, and now that she is slipping away, he decides to make a final effort to investigate their past.
The Government has ordered the Turkish Minister to Montenegro to make a final effort to explain to the Albanians Turkey's minimum concessions.
But Webber came close to winning the title last year and, at 34, may make a final effort as one of the older drivers on the grid.
At the meeting, the board agreed that Mr. Negroponte should make a final effort to end Intel's efforts to disrupt One Laptop's sales.
Well, summon your sinews and make a final effort: Alexander Watson's Ring of Steel is perhaps the most important of the current crop of books – and certainly one of the best.
Mr. Obama's foreign policy team is debating whether he should make a final effort after the November election to lay out terms of a possible peace agreement between Israelis and Palestinians.
At the White House, officials made a final effort to spur the committee on to a solution.
People were clambering onto the road, making a final effort to harass and block the column.
After General Campion (Roger Allam) arrives and assumes command, Christopher is sent to convalesce and ultimately returns home, where Sylvia makes a final effort to prevent him from pursuing a future with the willful young suffragist Valentine Wannop (Adelaide Clemens).
The school board in the long-troubled district in Roosevelt, N.Y., made a final effort today to stay in office, defending its record at a hearing presided over by the state official seeking its removal, Education Commissioner Richard P. Mills.
In mid-October, after a debate between "Here's the case" Republicans and "What was that case again?" Democrats, Congress will pass a resolution containing the big After: after the U.N. Security Council has made a final effort to insert unfetterable inspectors, and that fails, then the president will be authorized to enforce the terms of the 1991 surrender.
