The medals showing for each game should have this order:
1. 1st places, ranked by the number of participants in each tournament
2. The 2nd places, same as above
3. The 3rd, same as above
The other achievements are placed together in the start of the two rows.
This way, the profile for each game shows the best tournament achievements in an organized way, and the worst results 'drops' out of the two rows, when better results are achieved.
2nd option: The players could choose what medals to display... but I understand this option is asking too much... So I hope for the ranking system suggested first.