I'm fairly new to PERL and DBI, but from the standard examples I've been able to follow, this should work:
$dbh=DBI->connect($dbName, $dbUsername, $dbPassword);
$sql="UPDATE vs SET dc2='$fcriteria2' where dc2='$fcriterian'";
$Updaterecord=$dbh->do($sql)
# note: $fcriteria2 and $fcriteria are...