Do you mean you want the same query for all categories?
SELECT p.user_id, min(p.created_at) granted_at, MIN(p.id) post_id
FROM badge_posts p
JOIN topics t ON t.id = p.topic_id
WHERE (
SELECT count(*)
FROM post_actions pa
WHERE pa.post_id = p.id
AND post_action_type_id = (
SELECT id FROM post_action_types WHERE name_key = 'like'
) AND pa.user_id IN (
SELECT gu.user_id
FROM group_users gu
WHERE gu.group_id = ( SELECT id FROM groups WHERE name ILIKE '<GROUP>' )
)
) >= <MINIMUM LIKE COUNT>
AND p.user_id >= 0
GROUP BY p.user_id
HAVING count(*) >= <POST COUNT THRESHOLD>