Here's a simple method that doesn't require you to know what tags are in each section, or even what order the tags you are interested in appear. It is also easily extended to handle more tags of interest. The output is an array of hashes:

#! perl -slw
use strict;
use Data::Dump qw[ pp ];

my @accts;
{
    local $/ = 'TAGEND';
    while( <DATA> ) {
        m[
            (?=.* FIRSTNAME  \s+ ( \S+ ) )
            (?=.* LASTNAME   \s+ ( \S+ ) )
            (?=.* ACCOUNT    \s+ ( \S+ ) )
            (?=.* BILLAMOUNT \s+ ( \S+ ) )
        ]xsm and push @accts, {
            firstname => $1,
            lastname => $2,
            account => $3,
            billamount => $4,
        };
    }
}

pp \@accts;

__DATA__
[download]

TAGSTART
FIRSTNAME DAVID
LASTNAME RHODES
UNKNOWNTAG SOMEVALUE
UNKNOWNTAG SOMEVALUE
UNKNOWNTAG SOMEVALUE
ACCOUNT 1000901
UNKNOWNTAG SOMEVALUE
UNKNOWNTAG SOMEVALUE
BILLAMOUNT 4200
UNKNOWNTAG SOMEVALUE
TAGEND
TAGSTART
LASTNAME RHODES
UNKNOWNTAG SOMEVALUE
ACCOUNT 1000902
BILLAMOUNT 10000
UNKNOWNTAG SOMEVALUE
UNKNOWNTAG SOMEVALUE
FIRSTNAME MARY
UNKNOWNTAG SOMEVALUE
TAGEND
TAGSTART
FIRSTNAME BILL
LASTNAME HICKOK
UNKNOWNTAG SOMEVALUE
UNKNOWNTAG SOMEVALUE
ACCOUNT 1000903
UNKNOWNTAG SOMEVALUE
UNKNOWNTAG SOMEVALUE
UNKNOWNTAG SOMEVALUE
BILLAMOUNT 1200
TAGEND
TAGSTART
FIRSTNAME FRED
UNKNOWNTAG SOMEVALUE
LASTNAME BLOGGS
UNKNOWNTAG SOMEVALUE
ACCOUNT 1000909
UNKNOWNTAG SOMEVALUE
BILLAMOUNT -1
UNKNOWNTAG SOMEVALUE
TAGEND
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And the output:

C:\test>junk47.pl
[
  {
    account    => 1000901,
    billamount => 4200,
    firstname  => "DAVID",
    lastname   => "RHODES",
  },
  {
    account    => 1000902,
    billamount => 10000,
    firstname  => "MARY",
    lastname   => "RHODES",
  },
  {
    account    => 1000903,
    billamount => 1200,
    firstname  => "BILL",
    lastname   => "HICKOK",
  },
  {
    account    => 1000909,
    billamount => -1,
    firstname  => "FRED",
    lastname   => "BLOGGS",
  },
]
[download]

Could please point out any approach that would be the best to achieve this ?

What have you tried? What was the result?

The approach I'd take would be to create a pseudo state machine that changes state based on input. If I was able to attach graphics to a PM post I'd give you a nice state diagram for that, but here goes with a text only version

        +------------------------------------+
        |                                   yes
        v                                    |
     start----->"TAGSTART" ---> intag ---> "TAGEND?" <------+
                                             |              |
                                           process input ---+

The bit "process input" you essentially read in a line, depending on the tag you just add it to a hash as appropriate.

I suppose you mean "associative" array, that is a "hash" in Perl.

Instead of relying on nifty regexes to process whole records in one string I'd rather prefer using a flip-flop like demonstrated here: Re: Parsing file and joining content into string to read al tags from TAGSTART through TAGEND

in the if part do something like

   @tag = split ' ', $line, 2;
   $field{ $tag[0] } = $tag[1];
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and in the else part

   $bill{ $field{ACCOUNT} } = $field{BILLAMOUNT}  if %field;
   %field = ();
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IMHO this is a more robust and better maintainable approach.

UPDATE:

For instance if you ever need to retrieve all data per account just do

  $bill{ $field{ACCOUNT} } = { %field }  if %field;
  %field = ();
[download]

See also Re: print output from the text file. (marpa scanless dsl calculator), Re^2: Help with regular expression ( m/\G/gc ), perlfaq6#What good is \G in a regular expression?