Formal:
* Please review and edit this letter as you see fit.
* Kindly review and revise this letter as you deem appropriate.
* I would appreciate it if you could edit this letter according to your professional judgment.
Informal:
* Please take a look at this letter and make any edits you think are needed.
* Could you give this letter a quick edit?
* I'd love to get your feedback on this letter before I send it.
More specific:
* Please edit this letter for grammar and clarity.
* Could you make this letter more concise?
* Please review this letter for any factual errors.
Ultimately, the best way to phrase it depends on your relationship with the person you're asking and the specific type of edits you need.