The Code 13 Error is from Authorize.net. So we know that you are reaching Authorize.net but there is an issue with the credentials you sent. Please make sure you have entered valid credentials in your Forms>Settings>CIM page. That is the main Settings page under Forms - Not the feed settings under each individual form. (I know - it's confusing. But that is how Gravity Forms is set up and it works great once you're set up. :/) 
If you're having trouble after entering, please visit Authorize.net support for answers about Transaction Key generation. (FYI Sometimes people inadvertently enter their login information for their A.net account. That will not work. You need an API Login ID and a generated super secret Transaction Key.)
If you're having trouble after entering, please visit Authorize.net support for answers about Transaction Key generation. (FYI Sometimes people inadvertently enter their login information for their A.net account. That will not work. You need an API Login ID and a generated super secret Transaction Key.) Authorize.net looks at the email and customer ID. If you don't have a customer ID mapped in your feed settings, be sure to require and email address.
