I have my own preferences on how SQL should get tidied up, and what you have is close. However, you probably shouldn't expect perltidy to handle SQL as well as Perl. I'd run perltidy on the code, then go back and organize the SQL separately.

And my preference for formatting this chunk would be

my $sth = $dbh->prepare("
  SELECT t.id, t.emp_name, t.emp_email, t.req_status,
         t.date_requested, t.mngr_email,
         t.date_submitted, 
  ( SELECT GROUP_CONCAT (
    ( CASE WHEN req_status = 'Approved' THEN emp_name END )
        SEPARATOR ', ' )
    FROM  requests s
    WHERE s.date_requested = t.date_requested ) 
  AS approved 
  FROM requests t
  WHERE req_status      = 'Pending'
    AND mngr_email      = '$filter'
    AND date_requested >= '$date'
  ORDER BY emp_name, date_requested
");
[download]

This format highlights all of the key words, leaves spaces between each of the resulting columns, indents the 'AND' clauses to clarify the filtering, and generally exposes as much of the logic behind the query as possible.

There is no one right way to format SQL, but this approach seems fairly clear.