There are 14 Trophies that can be collected.

Bronze

Hat Trick
Score three goals in the same match on normal or hard difficulty with the same player

World Cup Champion
Win the World Cup with 4 teams

Nerves of Steel
Win on penalty kicks during extra time on normal or hard difficulty

On Tour
Play an online match

Destroyer
Win a match by a margin of at least five goals at the normal or hard difficulty

Brick Wall
Win the World Cup without letting a single goal in.

Football Scholar
Answer five questions correctly in a row in Quiz Match mode on normal or hard difficulty

Quiz Trick
Answer six questions correctly in a row on normal or hard difficulty in a single player match

Full Speed Ahead
Score a goal within 15 seconds from match start on normal or hard difficulty in a single player match

Keep on Fighting
Score in the last five seconds of a match on normal difficulty

Meeeedic!!!
Performed 100 successful tackles

International Player
Played a match with all teams

Silver

Football Einstein
Answer all questions correctly in a single player match on hard difficulty

Gold

World Cup Master
Win the World Cup with eight teams

http://www.ps3trophies.com/forums/playstation-trophy-news/12520-quizball-goal-trophy-list.html