Here is the full list of all 12 Catan trophies - there are 7 bronze, 4 silver and 1 gold.
Win a match where you have built 15 roads.
Win a match with all 5 victory point cards in your possession.
Win a match where you have collected fewer resources than everyone else.
Earn 11 victory points in a single match.
Win a "Quick Match" online.
Defeat three human opponents in a single online match.
Win a match with more victory points than your opponents combined.
Earn 12 victory points in a single match.
Win a match with at least 10 soldier cards.
Win a match where you have collected over 100 resources.
"Go Bust" 10 or more times in a single match.
Win a match where you have built 4 cities.