Is the issue that your direct manager can't write well or that s/he does not think you have demonstrated quality work? If it's the first, you can let them know how important this is to you and just request they have someone else proof it. If it's the second, do they have good reason to think this or is there just some issue between you two? I'd say point to your reviews, which hopefully indicate great work. You're going to need to address why your direct supervisor isn't writing your rec somewhere, so you should have you reason very clear in your head.

the expectation at a competitive program is that your recos are all exceptional. anything less is a red flag, since htat's what all of your competitors will be bringing to the table. i've written a basic primer to help you think thru the reco letter issue here: https://www.thefirstread.com/mba-admissi ... mendation/

kind of some basic stuff, but hope it's helpful nonetheless,
-james