Tu intento no estuvo tan lejos. Sin embargo, te faltaba una parte necesaria de la primera cláusula JOIN ... ON, y la segunda JOIN no es necesaria.
SELECT tbl1.stage_level_id, tbl1.max_value, MIN(s.moves) AS moves
FROM
(
SELECT stage_level_id, MAX(value) AS max_value
FROM scores
GROUP BY stage_level_id
) tbl1
LEFT JOIN scores s ON tbl1.stage_level_id = s.stage_level_id AND tbl1.max_value = s.value
GROUP BY stage_level_id