<?php
$url= "http://princesscoloringpages.blogspot.com/atom.xml?redirect=false&start-index=1&max-results=450";
$str = simplexml_load_file("$url");
foreach ($str->entry as $item)
{
$title = $item->title; // это работает
foreach ($item->category as $cat)
{
$category = $cat->attributes()->term;
echo "$category<br>\n";
}
}
?>