%newhash = reverse do { my $hash = reverse %myhash; %hash };
[download]

To get the keys only (which are the values in the reversed hash:

@unique_keys = do { my $hash = reverse %myhash; values %hash };
[download]

update: oops, got it all wrong. It' about getting all keys where duplicate values are found. As a single statement, formatted for readability

%myhash = (1 => 'a', 2=> 'b', 3=> 'a', 4=>'c',5 => 'b', 6 => 'a');
@k = do {
        my %s;
        map {
            my $v=$_;
            grep { $myhash{$_} eq $v} keys %myhash
        } grep {$s{$_}++==1} values %myhash
};
print "$_ => $myhash{$_}\n" for @k;
__END__
6 => a
1 => a
3 => a
2 => b
5 => b
[download]

Ah well. Readability... ;-)

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}