Blix Archive – Modifing the BX_archive function

I am trying to modify the archive functions for the Blix theme. Unfortunately I do not know enough about PHP to do this. Anyone out there that can help me or point me in the right direction?

Currently the code outputs this:
<h3><a href="link">Month Year</a></h3>
<ul class="postspermonth">
<li><a href="link">Post title</a> (Comment count)</li>
[..]
</ul>

I want it to output this:
<h3><a href="link">Category</a></h3>
<ul class="postspercategory">
<li><a href="link">Post title</a> (Comment count)</li>
[..]
</ul>

Here is the Code I am trying to edit:

function BX_archive() {
global $month, $wpdb;
$now = current_time('mysql');
$arcresults = $wpdb->get_results("SELECT DISTINCT YEAR(post_date) AS year, MONTH(post_date) AS month, count(ID) as posts FROM " . $wpdb->posts . " WHERE post_date <'" . $now . "' AND post_status='publish' AND post_password='' GROUP BY YEAR(post_date), MONTH(post_date) ORDER BY post_date DESC");
if ($arcresults) {
foreach ($arcresults as $arcresult) {
$url = get_month_link($arcresult->year, $arcresult->month);
$text = sprintf('%s %d', $month[zeroise($arcresult->month,2)], $arcresult->year);
echo get_archives_link($url, $text, '','
<h3>','</h3>
');
$thismonth = zeroise($arcresult->month,2);
$thisyear = $arcresult->year;
$arcresults2 = $wpdb->get_results("SELECT ID, post_date, post_title, comment_status FROM " . $wpdb->posts . " WHERE post_date LIKE '$thisyear-$thismonth-%' AND post_status='publish' AND post_password='' ORDER BY post_date DESC");
if ($arcresults2) {
echo "
<ul class=\"postspermonth\">
\n";
foreach ($arcresults2 as $arcresult2) {
if ($arcresult2->post_date != '0000-00-00 00:00:00') {
$url = get_permalink($arcresult2->ID);
$arc_title = $arcresult2->post_title;
if ($arc_title) $text = strip_tags($arc_title);
else $text = $arcresult2->ID;
echo "

• ".get_archives_link($url, $text, '');
  $comments = mysql_query("SELECT * FROM " . $wpdb->comments . " WHERE comment_post_ID=" . $arcresult2->ID);
  $comments_count = mysql_num_rows($comments);
  if ($arcresult2->comment_status == "open" OR $comments_count > 0) echo ' ('.$comments_count.')';
  echo "

\n";
}
}
echo "

\n";
}
}
}
}