If you wanted to do it using map you could do this:

my %hash;

map { push( @{ $hash{ $values{$_} } }, $_ ) } keys %values;
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which if you were golfing would save you a few characters on Roy Johnson's probably easier to read version:

while(my($k,$v)=each%values){push@{$hash{$v}},$k;}
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which becomes:

map{push(@{$hash{$values{$_}}},$_)}keys%values;
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and then access the result with:

for my $key (reverse sort keys %hash) {

    print "Level $key:\n", join(", ", @{$hash{$key}}), "\n\n";

}
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