use 5.010;  # say
use strict;
use warnings;

use Date::Manip qw( ParseDateString );

my @dates = (
   "Aug 8 12:12:13",
   "Jan 1 21:01:03",
   "Aug 8 12:12:14",
   "Aug 7 09:12:10",
);

my %lookup;
say $lookup{$_}
   for
      sort
      map { $lookup{ my $s = ParseDateString($_) } = $_; $s }
      @dates;