Create simple columned archive page

The best way is to make a SQL query to the database and get the results like the wp_get_archives() does but now you can manipulate the results as you wish.

In your case I would do something like this I added some comments to help you understand the process.

function get_archives_lists() {
    global $wpdb, $wp_locale;

    // get year month array
    $monthly = $wpdb->get_results("
        SELECT YEAR(post_date) AS year, MONTH(post_date) AS month
        FROM $wpdb->posts
        WHERE post_type="post" AND post_status="publish"
        GROUP BY YEAR(post_date), MONTH(post_date)
        ORDER BY post_date DESC
    ", ARRAY_A);

    // Rearrange the results to be [year][] = month so it will be easy to render
    $arr = [];
    array_map(function($item) use (&$arr) {
        $arr[$item['year']][] = $item['month'];
        return;
    }, $monthly);

    // loop years
    foreach($arr as $yearKey => $year) {
        ?>
        <div class="col-sm-2">
            <h2><a href="https://wordpress.stackexchange.com/questions/307058/<?php echo get_year_link($yearKey); ?>"><?php echo $yearKey; ?></a></h2>
            <ul>
            <?php
            // loop 12 for monthes
            for($m = 1; $m <= 12; $m++) {
                // get month name
                $month = sprintf( __( '%1$s' ), $wp_locale->get_month( $m ) );
                ?>
                <li>
                    <?php
                    // check if the month is in our results so we add a link to it.
                    if(in_array($m, $year)) {
                        ?>
                        <a href="<?php echo get_month_link($yearKey, $m); ?>"><?php echo $month; ?></a>
                        <?php
                    } else {
                        echo $month;
                    }
                    ?>
                </li>
                <?php
            }
            ?>
            </ul>
        </div>
        <?php
    }

}

You can see I used the bootstrap class col-sm-2 just for example you can use your own class and css.