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)
Play three "Pass Go" cards in a single turn (MONOPOLY DEAL)
Counter a "Just Say No" with a "Just Say No" card (MONOPOLY DEAL)
Never pay with properties during the game (MONOPOLY DEAL)
Be the first to have a full set (MONOPOLY DEAL)
Win a 6-player game (in local multiplayer) (MONOPOLY PLUS)
Collect a rent payment of more than 700 (MONOPOLY PLUS)
See the bank run out of houses (MONOPOLY PLUS)
Build your first hotel (MONOPOLY PLUS)
Get more than 100 thanks to a card (MONOPOLY PLUS)
Build your first house (MONOPOLY PLUS)
Complete two color sets in one trade (MONOPOLY PLUS)
Get one property of each color (MONOPOLY PLUS)
Own your first property (MONOPOLY PLUS)
Be the first player to start (MONOPOLY PLUS)