The majority of the time, when I need to get data that is stored in the database, depending on the situation, I tend to stick to database queries as they are more flexible.

You could use the following:

$db = JFactory::getDbo();
$query = $db->getQuery(true);

$query->select($db->quoteName(array('title')))
      ->from($db->quoteName('#__categories'))
      ->where($db->quoteName('parent_id') . ' = 1')
      ->where($db->quoteName('extension') . ' = ' . $db->quote('com_content'));
      
$db->setQuery($query);
$rows = $db->loadObjectList();

foreach ($rows as $row) 
{
    echo '<p>' . $row->title . '</p>';
}

As you can see, the parent_id must be 1 and the categories must belong to com_content (to prevent pulling categories from the likes of com_weblinks etc).

I've added in a little foreach loop to display the title of the category for each result.

Hope this helps

The majority of the time, when I need to get data that is stored in the database, depending on the situation, I tend to stick to database queries as they are more flexible.

You could use the following:

$db = JFactory::getDbo();
$query = $db->getQuery(true);

$query->select($db->quoteName(array('title')))
      ->from($db->quoteName('#__categories'))
      ->where($db->quoteName('parent_id') . ' != 0')
      ->where($db->quoteName('extension') . ' = ' . $db->quote('com_content'));
      
$db->setQuery($query);
$rows = $db->loadObjectList();

foreach ($rows as $row) 
{
    echo '<p>' . $row->title . '</p>';
}

This will get all categories for com_content apart from the very root category.

I've added in a little foreach loop to display the title of the category for each result.

Hope this helps