Successfully complete one of the following tasks to get a trophy:

Online Champion (Bronze): Win a match online against four human
opponents.
Sprinter (Bronze): Win a 'Quick Match' online.
Capitalist (Bronze): Win a match where you have collected over 100
resources.
Overachiever (Bronze): Earn 11 victory points in a single match.
Fortune's Fool (Silver): 'Go Bust' 10 or more times in a single
match.
Revolutionary (Silver): Win a match where you have collected fewer
resources than everyone else.