SELECT
Score.performerId, Performer.performerName,
Performer.countrycode, Country.countryName, Event.eventName, Score.points
FROM Score, Performer, Country, Event,
(
SELECT Performer.PerformerId, SUM(score.Points) TotalScore
FROM Score, Performer, Country, Event
WHERE roundName = 'Final'
AND Score.performerId=Performer.performerId
AND Performer.countryCode=Country.countryCode
AND Score.eventId=Event.eventId
group by Performer.PerformerId
order by TotalScore Desc
LIMIT 1
) MaxScore
WHERE roundName = 'Final'
AND Score.performerId=Performer.performerId
AND Performer.countryCode=Country.countryCode
AND Score.eventId=Event.eventId
AND Performer.PerformerId=MaxScore.PerformerId
Мне немного лень переходить на объединения в стиле ANSI, но вы должны начать использовать их в предпочтении перед запятой.