Bronze

First Wedge
Win your first wedge (Classic)

Full Circle
Fill your puck for the first time (Classic)

Classic Champ
Win a game of Classic Trivial Pursuit

On a Roll
String together 5 correct answers (Classic)

Keep on Rolling
Land on a roll again space twice in a row (Classic)

Fast Worker Entertainment
Acquire a Entertainment wedge on your first attempt (Classic)

Fast Worker Geography
Acquire a Geography wedge on your first attempt (Classic)

Fast Worker Science and Nature
Acquire a Science & Nature wedge on your first attempt (Classic)

Fast Worker History
Acquire a History wedge on your first attempt (Classic)

Fast Worker Sport and Leisure
Acquire a Sport & Leisure wedge on your first attempt (Classic)

Fast Worker Art and Literature
Acquire a Art & Literature wedge on your first attempt (Classic)

Wedge Off Winner
Win a Wedge Off (F&F)

Lucky Break
Win a wedge by betting (F&F)

Gambling Glory
Place 5 correct bets (F&F)

Risky Business
Use a Bonus Event for the first time (F&F)

Wedge HQ Winner
Win a wedge using the Wedge HQ space (F&F)

Bet Your Bottom Dollar
Win all your wedges by betting only (F&F)

Winner
Win a game of Facts & Friends

Cleared the Board
Clear the board

First Objective
Complete your first objective (CTB)

Objective Success
Complete 5 objectives (CTB)

Objective Champion
Complete 10 objectives (CTB)

Objective Master
Complete all objectives (CTB)

Maxed Out
Achieve a x10 multiplier on every category (CTB)

Personal Best
Break your own high score (CTB)

You don't know everything
Get a question wrong (Classic)

Maybe you don't know anything?
Get 5 questions wrong in a row (Classic)

Better luck next time
Be the first person to lose all their lives in the end game phase (F&F)

Silver

Unstoppable
String together 10 correct answers (Classic)

Gambling God
Place 10 correct bets (F&F)

Not a Scratch
Win the game without losing a life in the end game phase (F&F)

Domination
Win a 4 player game of Facts & Friends without losing a life

Flawless Entertainment
Answer all Entertainment questions correctly in a single game (F&F)

Flawless Art and Literature
Answer all Art & Literature questions correctly in a single game (F&F)

Flawless Science and Nature
Answer all Science & Nature questions correctly in a single game (F&F)

Flawless Sport and Leisure
Answer all Sport & Leisure questions correctly in a single game (F&F)

Flawless Geography
Answer all Geography questions correctly in a single game (F&F)

Flawless History
Answer all History questions correctly in a single game (F&F)

Straight To The Point
Clear the board using only the Wedge HQ spaces

Knowledge is Invaluable
Break 60,000 points (CTB)

You Were A Blur
Clear the board in under 10 minutes

Come on! You're not even trying!
Get 10 questions wrong in a row (Classic)

Gold

Wedge Domination
Win all the wedges in a single game (F&F)

You Know Too Much
Clear the board without getting a question wrong

Platinum Trophy

Platinum Trophy
Earn all other trophies

Source: http://www.ps3trophies.org

Edit: Formatting. ~Watchful