A little change to optimize that query (if you want to change the topic_id before execute it)
-- [params]
-- topic_id :topic_id = 18438
SELECT u.username
FROM badge_posts p
JOIN topics t ON p.topic_id = t.id
JOIN users u ON p.user_id = u.id
WHERE t.id = :topic_id
GROUP BY p.user_id,u.username
Note: replace 18438 for some topic_id from your forum
