Custom page template to display all image attachments

First, you need to create a custom page Template, to hold your custom loop output. Create a Theme file, named e.g. template-all-images.php, with the following header:

<?php
/**
 * Template name: All Images
 */
?>

Then, in the custom page template, you need to query for all image attachments. Try using WP_Query(), with post type/status arguments:

<?php
$images_query_args = array(
    'post_type' => 'attachment',
    'post_status' => 'inherit',
    'post_mime_type' => 'image'
);

$images_query = new WP_Query( $images_query_args );
?>

Then, output the query:

<?php
if ( $images_query->have_posts() ) : while ( $images_query->have_posts() ) : $images_query->the_post();

    // Normal loop output goes here

endwhile; endif;

// Be kind; rewind
wp_reset_postdata();
?>

For your loop output, if you just want to output a fully formed image, you can use e.g. wp_get_attachment_image():

<?php
wp_get_attachment_image( get_the_ID(), 'large' );
?>

(Replace 'large' with your desired image size, or omit, to use the default size, 'thumbnail'.)

The entire custom page template file might look like the following:

<?php
/**
 * Template name: All Images
 */

// Get the header
get_header();

// Image attachment query arguments
$images_query_args = array(
    'post_type' => 'attachment',
    'post_status' => 'inherit',
    'post_mime_type' => 'image'
);
// Query image attachments
$images_query = new WP_Query( $images_query_args );

// Image attachment query loop
if ( $images_query->have_posts() ) : while ( $images_query->have_posts() ) : $images_query->the_post();

    // Output the attachment image
    wp_get_attachment_image( get_the_ID(), 'large' );

endwhile; endif;

// Be kind; rewind
wp_reset_postdata();

// Get the footer
get_footer();
?>

Using your custom page template

1. Be sure that template-all-images.php is saved to your Theme directory under wp-content/themes/{theme-name}.
2. Create a new static page
3. Under the Page Attributes meta box, assign the “All Images” template to the page
4. Publish the page

Edits

Edits incorporated into the question.