There is more than one way to do it:

use strict;
use Text::CSV;

my $csv = Text::CSV->new ();
my %unique_records;

while (my $record = <DATA>) {
    $csv->parse($record) or die "Could not parse $record";
    my @columns = $csv->fields();
    s/.*=\s*(.*)/$1/ for @columns;
    print "$columns[0],$columns[1],$columns[4]\n" unless $unique_recor
+ds{$columns[1]}++ ;
}


__DATA__
Id=1,DE RecName: Full=anahnata,DE RecName: Full=deals,DE RecName: Full
+=buy, Type = cat
Id=2,DE RecName: Full=hahhhhaa,DE RecName: Full=sure,DE RecName: Full=
+sue, Type = dog
Id=3,DE RecName: Full=anahnata,DE RecName: Full=deals,DE RecName: Full
+=buy, Type = cat
Id=4,DE RecName: Full=hihahiha,DE RecName: Full=sure,DE RecName: Full=
+sue, Type = horse
Id=5,DE RecName: Full=anahnata,DE RecName: Full=deals,DE RecName: Full
+=buy, Type = cat
Id=6,DE RecName: Full=hahhhhaa,DE RecName: Full=sure,DE RecName: Full=
+sue, Type = dog
[download]

I added some duplicate records so you can see that indeed only the first of each duplicate record is printed.