You might see a problem with attachments that were added in Aha! and are duplicated multiple times in JIRA if the attachments field is not present in the Edit screen in JIRA.
Aha! can only set fields via the API that are visible on the Edit screen in the JIRA user interface. The Edit screen is the popup that you see when you click the "Edit" button on an issue.
Make sure that the attachments field is visible on the default screen in JIRA.