Your newer data shows that you usually have an array of "attribute" nodes, while I was assuming it would be a hash. I'm forcing XML::Simple to always make an array of the "attribute" nodes, and have changed the code to accomodate that.

use XML::Simple;

$data  = XMLin( \*DATA, KeepRoot => 1, ForceArray => [ qw/attribute/ ]
+ );

@attrs = map { $_->{category} }                        # We want the c
+ategory value 
         map { @{ $_->{attributes}{attribute} } }      # for each attr
+ibute
         values %{ $data->{dataschemas}{dataschema} }; # in all datasc
+hemas.

print "@attrs\n";

__DATA__
<dataschemas>
  <dataschema name="varyingName1">
   <attributes>
    <attribute category="one" fair="no" />
   </attributes>
  </dataschema>
  <dataschema name="varyingName2">
     <attributes>
        <attribute category="" parser="CSVParser" />
        <attribute category="APS" internalCategory="aps" />
        <attribute category="ASC" internalCategory="asc" />
        <attribute category="ASMT" internalCategory="asmt" />
        <attribute category="LE" internalCategory="l&amp;e" />
        <attribute category="NCO" internalCategory="nco" />
        <attribute category="NEED TITLE" internalCategory="need title"
+ />
        <attribute category="New Need ID" internalCategory="need id" /
+>
        <attribute category="SUMMARY OF DELIVERABLES" parser="TextPars
+er" extract="true" segmentation="hard" />
    </attributes>
  </dataschema>
</dataschemas>
[download]

A version based on the foreach / while idea:

foreach my $dataschema ( values %{ $data->{dataschemas}{dataschema} } 
+)
{
    foreach my $attr ( @{ $dataschema->{attributes}{attribute} } ){
        print "category is: ",
              $attr->{category},
              "\n";
    }
}
[download]