Add field 'downloaded' (int 10 default 0) to mantis_bug_file_table
bug_api.php, function bug_get_attachments, add field downloaded
file_api, function file_get_visible _attachments add the lines :
$t_downloaded = $t_row['downloaded'];
$t_attachment['downloaded'] = $t_downloaded;
just before 'if( $t_can_download ) {'
file_download.php, add the following lines:

Update download counter

$query2 = "update $t_bug_file_table set downloaded=downloaded+1 WHERE id=" . $v_id;
$result2 = db_query_bound( $query2 );
just after (line 75):
if ( !file_can_download_bug_attachments( $v_bug_id ) ) {access_denied();}
Last change in print-api.php, function print bug_attachment_list. add the line:
$t_downloaded = $t_attachment['downloaded'] ;
just after "$t_date_added="
Finally change the actual line that prints the attachment with:
echo $t_href_end . ' ' . $t_href_start . $t_file_display_name . $t_href_end . $t_href_clicket . ' (' . $t_filesize . ' ' . lang_get( 'bytes' ) . ') ' . '<span class=\"italic\">' . $t_date_added . ' Downloaded: '. $t_downloaded . ' time(s)</span>';