There are 49 Trophies that can be collected.

Bronze

Arcade Beginner    
Clear a stage in Arcade Mode     

Doubles Beginner    
Clear a stage in Arcade Mode Doubles     

Grand Slammer    
Clear Singles Mode    

Doubles Grand Slammer    
Clear Doubles Mode

Balloon Popper    
Pop 30 balloons in Practice Mode    

Exhibitionist     
Play 10 Exhibition Matches    

In Your Face Tennis!     
Win 5 VR matches    

Screen Sharer     
Play a Touch VS game    

Classic Photographer    
Take a classic photo with VT CAM    

Great Sniper    
Achieve a 5x Combo in Clay Shooting     

Mother Hen    
Deliver at least 10 chicks simultaneously to their mother in Egg Collector     

Hat Tricker    
Score 3 goals in a row in Ace Striker

Bomb Fiend    
Detonate 20 bombs in the opponent's court in Bomb Match     

Moneybags    
Collect 1000 coins in Coin Match     

Wind Master    
Pop 3 balloons in one Wind Match     

Wall Whiz    
Hit a wall 5 times with the ball in one Wall Match     

Turkey Bowler    
Get a turkey in Pin Crusher    

Emergency Stop    
Stop the ships 10 times in Rock the Boat    

World Tour Cleared!    
Clear the game    

Famous    
Become: Famous

Future Champion    
Win the final tournament of the Tour Break    

Look Alike    
Create a player by taking a picture    

Regular Customer    
Stop at the Management Office 30 times

International Traveler    
Play an online visitor 10 times    

Tycoon    
Earn 1,000,000 in total prize money

Shopeholic    
Purchase 50 types of items in the Kit Catalouge    

Online Debut    
Play online with a customised character    

First Online Victory    
Win a match online    

Online Streak     
Win three consecutive matches online

Loving It!     
Win 10 Love games

Endless Rally!    
Sustain a rally for 30 shots

Marathon Runner    
Run 42km (26mi)    

Swing Machine    
Swing 5000 times    

Best Stroker    
Win 100 points with ground strokes    

Volley Master     
Win 100 points with volleys    
    

Pro-Tennis Fan    
Play using all the real tennis players    

Full Swing!     
Hit 50 MAX power shots    

Breakthrough     
Win 10 games as the receiving player

Silver

Great King    
Defeat the King in Arcade Mode Singles

Poker Face    
Get 10 royal straight flushes in Royal Poker

Accomplished     
Become: Accomplished

Top Condition    
Reach a Condition level of 20

Big Hitter    
Hit 250 MAX Serves    

Power Smash!    
Hit 250 smashes

Super Player    
Hit 100 super shots

Gold

Ticket to the SPT Finals     
Make it to the playoffs

Jack of all Trades     
Take lessons for all play styles

Online Master    
Reach Rank A

Platinum

Tennis God    
Collect every trophy

http://www.ps3trophies.org/game/virtua-tennis-4-world-tour-edition/trophies/