I've tried many ways to obtain this info but failed. I'm using the library JSON::PP and function decode_json.

It would be best if you showed us what you tried and how it failed (SSCCE), because otherwise we can't tell if you're just asking us do your homework for you or (ab)using us as a code writing service. But since this was a nice little excercise, here's a freebie...

use warnings;
use strict;
use JSON::PP qw/decode_json/;

# search a data structure recursively for a specific hash key
# and return its "path" as a string if it is found
sub get_path_by_key {
    my ($data, $search_key) = @_;
    # an array of the data items left to search, each being a hash
    # with keys "d" for the data item and "p" for the item's path:
    my @to_search = ( { d=>$data, p=>[] } );
    while (@to_search) {
        # get the item we're currently inspecting:
        my $cur = shift @to_search;
        if ( ref $$cur{d} eq 'ARRAY' ) {
            # if the data item is an array, go through its indices
            for my $i ( 0 .. $#{$$cur{d}} ) {
                # skip any array values that aren't nested data:
                next unless ref $cur->{d}[$i];
                # put each of the array's values on the search list
                push @to_search, { d=>$cur->{d}[$i],
                    # this means the output won't include indices:
                    p=>$$cur{p} };
                    # this would be one way to include indices:
                    #p=>[ @{$$cur{p}}, "[$i]" ] };
            }
        }
        elsif ( ref $$cur{d} eq 'HASH' ) {
            # if the current data item is a hash,
            # first check if it contains the search key:
            if ( exists $cur->{d}{$search_key} ) {
                # this builds the return value string:
                return join '.', @{$$cur{p}}, $search_key;
            }
            # otherwise, go through the hash's keys:
            for my $k ( sort keys %{$$cur{d}} ) {
                # skip any hash values that aren't nested data:
                next unless ref $cur->{d}{$k};
                # put each of the hash's values on the search list
                push @to_search, { d=>$cur->{d}{$k},
                    p=>[ @{$$cur{p}}, $k ] };
            }
        }
    }
    return  # return nothing in case the key isn't found
}

# this is just an idiom to read the whole __DATA__ section:
my $json = do { local $/; <DATA> };
# decode the JSON string into a Perl data structure:
my $data = decode_json($json);
# use our function:
my $path = get_path_by_key($data, 'Obj11AttributesObj1Key1');
print "path=$path\n";

__DATA__
[ {
    "Obj1": [ {
        "Obj11Id": "Id11",
        "Obj11Version": "v1",
        "Obj11Attributes": {
            "Obj11AttributesObj1": {
                "Obj11AttributesObj1Key1": "1",
                "Obj11AttributesObj1Key2": "3"
            },
            "Obj11AttributesObj2": {
                "Obj11AttributesObj2Key1": "9"
            }
        }
    }, {
        "Obj12Id": "Id12",
        "Obj12Version": "v1",
        "Obj12Attributes": {
            "Obj12AttributesObj1": {
                "Obj12AttributesObj1Key1": "2",
                "Obj12AttributesObj1Key2": "4"
            },
            "Obj12AttributesObj2": {
                "Obj12AttributesObj2Key1": "8"
            },
            "Obj12AttributesArray1": [ {
                "Obj12AttributesArray1Obj1Key1": 1
            } ]
        }
    } ]
}, {
    "Obj2": [ {
        "Obj21Id": "Id21",
        "Obj21Version": "v1",
        "Obj21Attributes": {
            "Obj21AttributesObj1": {
                "Obj21AttributesObj1Key1": "3",
                "Obj21AttributesObj1Key2": "5"
            },
            "Obj21AttributesObj2": {
                "Obj21AttributesObj2Key1": "7"
            }
        }
    }, {
        "Obj22Id": "Id22",
        "Obj22Version": "v1",
        "Obj22Attributes": {
            "Obj22AttributesObj1": {
                "Obj22AttributesObj1Key1": "4",
                "Obj22AttributesObj1Key2": "6"
            },
            "Obj22AttributesObj2": {
                "Obj22AttributesObj2Key1": "0"
            },
            "Obj22AttributesArray1": [ {
                "Obj22AttributesArray1Obj1Key1": 1
            } ]
        }
    } ]
} ]
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If you're new to Perl you'll probably need perlreftut to understand much of the code.