There are 46 Trophies that can be collected.

Bronze

1st Bid FTW    
Win a Contestant's row for the first time (Single player).    

Archive Rookie    
Unlock your 1st tape.    

Archive Explorer    
Unlock 5 tapes.    

Archive Lover    
Unlock 15 tapes.    

Archive Specialist    
Unlock 30 tapes.

Social Player    
Play a show online (any game mode).

The Contestant    
Play 5 Contestant's Row online (any game mode).

The Veteran    
Play 30 games online (any game mode).    

Hospitality    
Host 10 games online (any game mode).

Let's get the party started    
Play a local multiplayer game.    

Big Winner    
The host player must finish 1st on a 4 players local multiplayer game.    

Party Animal    
Play 10 Local multiplayer games.

Lucky Chips    
Plinko 1983 : The host player wins $15 000 or more in a Plinko game (Local multiplayer).    

Movie Night    
Watch a bonus video.    

Videophile    
Watch all bonus videos.    

The 70s Fan    
Play 50 pricing games in 70's Decade (Single Player) (Show or Pricing game).    

The 80s Fan    
Play 60 pricing games in 80's Decade (Single Player) (Show or Pricing game).    

The 90s Fan    
Play 60 pricing games in 90's Decade (Single Player) (Show or Pricing game).    

The 00s Fan    
Play 70 pricing games in 00's Decade (Single Player) (Show or Pricing game).

Silver

Archive Master    
Unlock all the tapes.

Drop it like it’s hot    
Plinko 1998 : Win $30,000 or more in one Plinko game online (any game mode).    

The Athlete    
Hurdles : Win 3 Hurdles games online (any game mode).    

The Champion    
Finish 1st on 10 multiplayer games online (any game mode).

Serious Player    
Finish 1st on five 4-players multiplayer games online (any game mode).

On the nose!    
Make 3 exact bids on Contestant's row (Any game mode).

Big Fred    
The host player wins a Double Money Showcase in a local multiplayer game.

Gold

Showcase Master    
Win every showcases of every shows.

Awesomeness    
Showcase Showdown : Win by landing twice on 100 on your first spin and on your bonus spin.

Platinum

The Ultimate Fan    
Win all the other trophies.

17 Secret

Bronze

The Finish Line    
SECRET – Win $10,000 cumulative in Race Game (Single player)    

The PhD    
SECRET – Professor Price : Answer correctly 3 questions in a row in one game. (Single)    

Punched!    
SECRET – Punch A Bunch : Win $50,000 (cumulative) (Single)    

Get it rollin’    
SECRET – Super Ball : Win $60,000 (cumulative) (Single)

Somewhere over the rainbow    
SECRET – Golden road 1984 : Win $50,000 (cumulative) (Single)    

The pot of gold    
SECRET – Golden road 2005: Win $200,000 (cumulative) (Single)    

Superstar    
SECRET – Walk Of Fame : win $20,000 (cumulative) (Single)    

My name is Tiger    
SECRET – Hole in One : win $40,000 (cumulative) (Single)

Shopaholic    
SECRET – It's in the bag : Win $40,000 (cumulative) (Single)

It’s a Kind of Magic    
SECRET – Magic Number : win $10,000 (cumulative) (Any Magic Number) (Single)

Silver

A Nickel Away    
SECRET – Check Out : Win the game with a difference of $0.05 or less (1982 or 1996) (Single)

Conquer the maze    
SECRET – Pathfinder : win a Pathfinder game without making any mistake (Single)    

On the Edge    
SECRET – Cliff Hangers : win with the cliffhanger standing on the 25th step of the mountain. That was close! (Any Cliff Hangers) (Single)

No strikes    
SECRET – 3 Strikes 2009 : Win a game without drawing an X (Single)    

Homerun!    
SECRET – 3 strikes 1999 : win a game without misplacing any number (Single)    

The Clairvoyant    
SECRET – Cover Up : win by placing all the right numbers in your first try (Single)    

Time to Go Bonkers!    
SECRET – Bonkers : Win a game on your first try! (Single)

http://www.ps3trophies.org/game/the-price-is-right-decades/trophies/