Proof of concept: Award a badge to anyone with badges 106, 107, and 108.
SELECT user_id, CURRENT_TIMESTAMP granted_at, NULL post_id
FROM user_badges pb
WHERE badge_id = 106
AND EXISTS (
SELECT 1 FROM user_badges ib
WHERE pb.user_id = ib.user_id
AND ib.badge_id = 107
)
AND EXISTS (
SELECT 1 FROM user_badges ib
WHERE pb.user_id = ib.user_id
AND ib.badge_id = 108
)
;