From the OP:

I can access each element by using @Data[$_]{ID}, @Data[$_]{Score}...

I assume this was a misprint for $Data[$_]{ID}, $Data[$_], since you are accessing single elements, not array slices.

it's array of array of hashes and chorobas code works.

Here is how choroba’s code works for me:

use strict;
use warnings;

my @data =
(
    { ID => 'AA', Score => 20 },
    { ID => 'D',  Score => 30 },
    { ID => 'F',  Score =>  7 },
    { ID => 'AA', Score =>  3 },
);

## choroba's solution:

my %by_id;
push @{ $by_id{ $_->{ID} } }, $_->{Score} for @data;

# Sort the scores for each id.
$_ = [ sort { $b <=> $a } @$_ ] for values %by_id;

# Sort the ids by the highest score.
for my $id (sort { $by_id{$b}[0] <=> $by_id{$a}[0] } keys %by_id) {
    print "ID: $id\tScore: $_\n" for @{ $by_id{$id} };
}
[download]

As you can see, there is only one array; i.e., @data is an array of hashes (AoH).

Hope that helps,