In the canonical solution for finding unique elements a hash is employed since the keys are guaranteed to be unique. You simply need two hashes; one top-level (snake, bird), and one deeper level (scales, fangs, tail). But then once you've used that deeper level hash to remove the duplicate attributes, you can convert its keys to the contents of an anonymous array referred to by the top-level hash. In other words, you can replace the lower level hash with an array containing the keys that lower level hash once held.

#!/usr/bin/env perl

use strict;
use warnings;
use Data::Dumper;

my %hash;

while (<DATA>) {
    chomp;
    my ($k, $v) = split /\s/;
    $hash{$k}{$v} = undef;
}

$hash{$_} = [keys %{$hash{$_}}] for keys %hash;

print Dumper \%hash;

__DATA__
bird beak
bird beak
bird claw
bird wings
bird feathers
snake fangs
snake scales
snake fangs
snake tail
[download]

The output will be:

$VAR1 = {
          'snake' => [
                       'tail',
                       'fangs',
                       'scales'
                     ],
          'bird' => [
                      'claw',
                      'wings',
                      'beak',
                      'feathers'
                    ]
        };
[download]

Another approach could be to track whether an attribute pair has been seen before in realtime during the while loop, rather than postprocessing the hash of hashes into a hash of arrays. To do this you could use a temporary %attribseen hash where the keys are some unique concatenation of the animal type and a given attribute of that animal. For example, 'bird' and 'beak' could be used to form a hash key of bird|beak, and then you use that to assure uniqueness:

my %hash;

{
    my %attribseen;
    while (<DATA>) {
        chomp;
        my ($k, $v) = split /\s/;
        push @{$hash{$k}}, $v unless $attribseen{"$k|$v"}++;
    }
}

print Dumper \%hash;

__DATA__
bird beak
bird beak
bird claw
bird wings
bird feathers
snake fangs
snake scales
snake fangs
snake tail
[download]

The output will be the same as before. For some this may be simpler to look at. Even better (from a legibility standpoint) may be to separate out the uniqueness check into its own object, which can offer some internal state:

#!/usr/bin/env perl

package PairUnique;

use strict;
use warnings;

sub new {return bless {}, shift}

sub unique {
    my ($self, $k, $v) = @_;
    return !$self->{"$k=>$v"}++ ? $v : ();
}

package main;

use strict;
use warnings;
use Data::Dumper;

my %hash;
{
    my $get = PairUnique->new;
    while (<DATA>) {
        chomp;
        my ($k, $v) = split /\s/;

        my $aref = $hash{$k} //= [];

        push @$aref, $get->unique($k,$v);
    }
}

print Dumper \%hash;

__DATA__
bird beak
bird beak
bird claw
bird wings
bird feathers
snake fangs
snake scales
snake fangs
snake tail
[download]

This separates out the uniqueness logic, and keeps only the structure-building logic inside the while loop. More code means more to maintain and understand, but it's possible that intent will be clearer to the person reading the code.

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