There are 41 trophies that can be collected.

Bronze

Winner
Win your first game of MONOPOLY Streets

Lucky Three
Rolled Triples

Building the Empire
Won 10 offline games

No Ground Untouched
Player has built 100 houses

Expensive Property
Acquire the most expensive property in the game

Eviction Notice
Replaced your housrs with a hotel

Bypass Bail
Rolled doubles to get out of Jail for free

Needs a New Challenge
Successfully won against 3 hard AI

Philanthropist
Completed a trade that gave another player a color group

Flea Market
Bought a property cheaply

Celebrating 75
Acquired your 75th property

Repeat Offender
Went to jail for the 3rd time in one game

Glad its not my Bill
Received 120 on a Utility rent

Better than Free
Received more than 200 when landing on Free Parking

I Like Trains
Own all the railroads

Great Start
Someone pays you rent before your second turn

Market Inflator
Get an opponent to pay double the price during an auction

Now that is ROI
Collect more than a 1000 in rent

I'm Keeping this Card
Player paid to get out of Jail when they had a Get out of Jail Free Card

Tax Audit Nightmare!
Paid 1200 in Taxes in one game

Doesn't hurt much
Paid the smallest rent in an online game

Plays Nicely with Others
Finished an online game

Better Luck Next Time
Bankrupted another player online

I Want a Rematch
Lost to another player online

How We Played Back in my Day
Finished an online game using custom house rules

Next Rung on the Ladder
Bankrupted a higher ranked player

Silver

Subdivision
Player has built 500 houses

Mega-Tycoon
Finished a game with total worth greater than 9000

Quick Win
Won a game in under 20 minutes

Property Magnate
Own 3 color groups at once

This Plan is Better
Completed a trade that gave you a color group

Rolled a 15
Player rolled a 15

Hotel Maximus
See the bank run out of hotels in a game with Official MONOPOLY rules

All Your Eggs in One Basket
The only properties owned are part of a single color group

I can do this without Houses
In an online game, own all the railroads and utilities

Taking Over the World
10 online game wins

Gold

So Big and Shiny
Get the largest upgrade to your corporate HQ

Rainbow
Own one of each color group at the same time

Concierge Service
Provide the best Hotel Service on the most expensive property without a player going bankrupt

Auctioneer
Player has won 50 online auctions

Platinum

Platinum Trophy
Win all trophies

http://www.ps3trophies.org/game/monopoly-streets/trophies/