@GoDemonDeacons I just went through this process due to N-number change. E-mail your local FSDO. They will get back to you. The person that contacted me sent me a very detailed list explaining what I needed to you. In short, you must upload a scanned letter, signed by the owner(s) of the aircraft explaining why you need an A/W Cert. Valid reasons include lost, damaged, N-number change. They might want you to upload some documentation like that scan from your log book. Here's an excerpt from what they sent me:
First step is to go to the following website and complete your application for replacement Airworthiness Certificate: https://awc.faa.gov/AWCExternalApplicant/Splash/Index
Please note, registration will require setting up a two-factor authenticate (2FA) credential.
Click 'Agree,' button at the bottom left of the login page.
Click 'New User Sign-Up,' IF you are not already registered for 2FA in MyAccess
Click 'Login,' at top of this page AFTER setting up 2FA credential
Complete Replacement Certificate application process in AWC, the ‘Help,’ button at the upper right-hand side of page is helpful if you have questions completing your application
You will also need the following documents to upload to your application in AWC:
Signed statement detailing nature of need for replacement certificate, SIGN the statement before upload. If lost, make sure this is detailed in said statement. Note: Completed FAA Form 8130-6 IS NOT required for a replacement Airworthiness Certificate.
etc.