Your example doesn't seem to be a good one because the histogram for most is "1". Is this what you are intending?

#!/usr/bin/perl
use warnings;
use strict;
use Data::Dumper;

my @AoA =( [qw(TTVVRRRDR KFRQLLWFH RSQSPRRRR CSPHHTALR WIRTPPAYR VVRRR
+DRGR HISCLTFGR RTPSPRRRR NTNMGLKFR LVSFGVWIR)],
           [qw(AILCWGELM TVLEYLVSF GLKFRQLLW LSFLPSDFF LLSFLPSDF LLWFH
+ISCL MQLFHLCLI QLFHLCLII ATVELLSFL ALRQAILCW)],
           [qw(TTVVRRRDR CSPHHTALR WIRTPPAYR NVNMGLKIR LVSFGVWIR HISCL
+TFGR)],
           [qw(CSPHHTALR YVNTNMGLK WIRTPPAYR TLPETTVVR HISCLTFGR NTNMG
+LKIR WGMDIDPYK LVSFGVWIR)],
         );

#calculate histogram

my %histo;

foreach my $rowref (@AoA)
{
   foreach my $elem (@$rowref)
   {
      $histo{$elem}++;
   }
}

print Dumper \%histo;

#sort each array according to the histogram

foreach my $rowref (@AoA)
{
   @$rowref = sort{my $A = $histo{$a};
                   my $B = $histo{$b};
                      $A <=> $B} @$rowref; #edit guess should be $B<=>
+$A

}

print Dumper \@AoA;

__END__
$VAR1 = {
          'WGMDIDPYK' => 1,
          'YVNTNMGLK' => 1,
          'MQLFHLCLI' => 1,
          'KFRQLLWFH' => 1,
          'HISCLTFGR' => 3,
          'NTNMGLKIR' => 1,
          'LVSFGVWIR' => 3,
          'QLFHLCLII' => 1,
          'VVRRRDRGR' => 1,
          'WIRTPPAYR' => 3,
          'LLSFLPSDF' => 1,
          'TVLEYLVSF' => 1,
          'CSPHHTALR' => 3,
          'NTNMGLKFR' => 1,
          'LLWFHISCL' => 1,
          'LSFLPSDFF' => 1,
          'AILCWGELM' => 1,
          'TTVVRRRDR' => 2,
          'NVNMGLKIR' => 1,
          'RSQSPRRRR' => 1,
          'ALRQAILCW' => 1,
          'GLKFRQLLW' => 1,
          'ATVELLSFL' => 1,
          'TLPETTVVR' => 1,
          'RTPSPRRRR' => 1
        };
$VAR1 = [
          [
            'KFRQLLWFH',
            'RSQSPRRRR',
            'VVRRRDRGR',
            'RTPSPRRRR',
            'NTNMGLKFR',
            'TTVVRRRDR',
            'CSPHHTALR',
            'WIRTPPAYR',
            'HISCLTFGR',
            'LVSFGVWIR'
          ],
          [
            'AILCWGELM',
            'TVLEYLVSF',
            'GLKFRQLLW',
            'LSFLPSDFF',
            'LLSFLPSDF',
            'LLWFHISCL',
            'MQLFHLCLI',
            'QLFHLCLII',
            'ATVELLSFL',
            'ALRQAILCW'
          ],
          [
            'NVNMGLKIR',
            'TTVVRRRDR',
            'CSPHHTALR',
            'WIRTPPAYR',
            'LVSFGVWIR',
            'HISCLTFGR'
          ],
          [
            'YVNTNMGLK',
            'TLPETTVVR',
            'NTNMGLKIR',
            'WGMDIDPYK',
            'CSPHHTALR',
            'WIRTPPAYR',
            'HISCLTFGR',
            'LVSFGVWIR'
          ]
        ];
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