Display all posts from selected month

You can use the pre_get_posts action to set posts_per_page to -1 on the monthly archive pages.

I said wrongly in a comment to use is_archive() as your conditional. The problem with is_archive() is, it returns true on all archives, which includes category and taxonomy archive pages as well.

I would suggest to make use of is_date() and is_month() if you specifically needs to target montly archives

(Please note, the following code is untested and needs PHP 5.3+)

add_action( 'pre_get_posts', function ( $query ) {
    if ( !is_admin() && $query->is_date() && $query->is_month() && $query->is_main_query() ) {
        $query->set( 'posts_per_page', '-1' );
    }
});