JSON API needs to be customized a bit to retrieve *all* the image attachments in a WordPress site.

functions_attachments.php

// Add this snippet of code to functions.php if you want to retrieve all
// the attachments on a blog using the JSON API plugin.

// Use this API call: http://foo.com/?json=core.get_posts&post_type=attachment

add_action('json_api-core-get_posts', 'setup_attachments_filter');
function setup_attachments_filter() {
  // Workaround for JSON API disallowing post_status arguments
  global $json_api;
  if ($json_api->query->post_type == 'attachment') {
    add_action('pre_get_posts', 'allow_inherit_status');
    add_filter('json_api_encode', 'encode_attachment_data');
  }
}

function allow_inherit_status($wp_query) {
  // Attachments inherit their post_status from whatever they're attached to.
  $wp_query->query_vars['post_status'] = 'inherit';
}

function encode_attachment_data($data) {
  // Returned attachment posts need to have the image URLs encoded.
  global $json_api;
  foreach ($data['posts'] as $index => $post) {
    $data['posts'][$index] = $json_api->introspector->get_attachment($post->id);
  }
  return $data;
}