This is a WP_Query + original loop with post thumbnail archive.

archive.php

<?php get_header(); ?>

	<article>
		<div class="left">
			<h3>Categories used on the website</h3>
			<div class="cat-listing">
				<span class="category-name">Category name</span><span class="times-used">Times used</span>
				<p>
				<?php
					$args = array(
						'show_count' 		=> true,
						'use_desc_for_title' 	=> false,
						'title_li' 		=> '',
						'hide_empty' 		=> 0,
						'style' 		=> '',
						'separator' 		=> '',
					);
					wp_list_categories($args);
				?>
				</p>
			</div>
			<?php
				$current_year = the_date('Y');
				$post_title_arguments = array(
					'post_type' 		=> 'post',
					'post_status' 		=> 'publish',
					'posts_per_page' 	=> -1,
					'orderby' 		=> 'ASC',
					'date_query' 		=> array('year' => $current_year)
				); $post_title_query = new WP_Query($post_title_arguments); ?>

				<h3>This years posts by title</h3>

				<span class="category-name">Entry title</span><span class="times-used">Comments</span>

				<?php if($post_title_query->have_posts()) { while($post_title_query->have_posts()) { $post_title_query->the_post(); ?>

					<p class="post-title"><a href="<?php the_permalink(); ?>"><?php echo wp_trim_words(get_the_title(), 8, '...'); ?></a><span><?php echo $post->comment_count; ?></span></p>

				<?php } ?>

			<?php } wp_reset_postdata(); ?>

		</div><!-- /left -->
		<div class="right">
			<div class="thumbnail-archive">

				<h2><?php single_cat_title(); ?></h2>

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

					<p style="background-image: url('<?php echo wp_get_attachment_url( get_post_thumbnail_id( $post->ID ) ); ?>');"><a href="<?php the_permalink(); ?>">&nbsp;</a></p>

				<?php endwhile; else : echo '<h2>No content found</h2>'; ?>

			</div>
		</div><!-- /right -->
	</article>

<?php endif; get_footer(); ?>

You can see it live here: http://www.harshclimate.com/archives/