The documentation for the Char handler says this:

A single non-markup sequence of characters may generate multiple calls to this handler

So you need to accumulate the data and only print it in the end handler. Something like this perhaps:

use strict;
use XML::Parser;
my $parser = new XML::Parser(ErrorContext => 2);

my $xmlStr = "<data>
<Company_Name>XYZ CMPNY</Company_Name>
<ArgId>775340</ArgId>
<First_Name>Carol &amp; Jerry</First_Name>
</data>";

my $writeDataFlag = 0;

$parser->setHandlers(
   Start => \&start_handler,
   Char => \&char_handler,
   End => \&end_handler);

$parser->parse($xmlStr);

my $text;

sub char_handler {
  my ($p, $data) = @_;
  if ($writeDataFlag) {
    $text .= $data;
  }
}

sub start_handler {
  my ($p, $data) = @_;
  if($data =~ /^(Company_Name|First_Name)$/) {
    $writeDataFlag = 1;
  }
}

sub end_handler {
  my ($p, $data) = @_;
  if ($writeDataFlag) {
    print "Data - [$text] \n";
    $text = '';
    $writeDataFlag = 0;
  }
}
[download]