To download attachment files the attachment id is required. Get the id through the MgmtAttachment. The getItemDeep populate the MgmtItem with attachments
MgmtItem item = con.getItemDeep(parentid, id);
int count = item.getAttachmentCount();
MgmtAttachment att = item.getAttachment(0);
Still the actual attachment file must be downloaded with a separate method.
The second parameter is the id of the attachment and the last is a file path which will be the name of the downloaded
con.getFile(parentid, att.getId(), "c:\\temp\\myfile.txt");