Disclaimer: I don't have any setup for testing any of this with, but here's some skeleton code:

use Mail::Box::POP3;

my $folder = Mail::Box::POP3->new(folder => $ENV{MAIL}, ...);
my $message = $folder->message(0);

if($message->body->isMultipart) {
    foreach my $part ($message->body->parts) {
        my $attached_body = $part->decoded;
        ...
    }
}
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This is based on pieces of code found throughout the (admittedly ascetic) Mail::Box documention.