You could use a handler:

use XML::Twig;
use strict;
use warnings;

my $twig = XML::Twig->new(twig_handlers => { Day => \&Day });
$twig->parsefile('CC.xml');
exit;

sub Day {
    my ( $twig, $day ) = @_;
    if ($day->att('day-of-week') eq 'Tuesday') {
        print $day->first_child('Times')->first_child('Time')->att('st
+art-time'), "\n";
    }
}

__END__

02:00
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