Here is the full list of all 15 Monopoly Family Fun Pack trophies - there are 13 bronze, 1 silver and 1 gold.
Use 5 "Rent" cards during a game (MONOPOLY DEAL)
See the bank run out of houses (MONOPOLY PLUS)
Counter a "Just Say No" with a "Just Say No" card (MONOPOLY DEAL)
Play three "Pass Go" cards in a single turn (MONOPOLY DEAL)
Win a 6-player game (in local multiplayer) (MONOPOLY PLUS)
Get more than 100 thanks to a card (MONOPOLY PLUS)
Complete two color sets in one trade (MONOPOLY PLUS)
Never pay with properties during the game (MONOPOLY DEAL)
Be the first to have a full set (MONOPOLY DEAL)
Get one property of each color (MONOPOLY PLUS)
Collect a rent payment of more than 700 (MONOPOLY PLUS)
Build your first hotel (MONOPOLY PLUS)
Build your first house (MONOPOLY PLUS)
Own your first property (MONOPOLY PLUS)
Be the first player to start (MONOPOLY PLUS)