There are 20 Trophies that can be collected.

Bronze

Feel The Power    
Overdrive a shot.     

In a Spin    
Use spin control whilst the ball is in flight.     

Retail Therapy    
Purchase an item from the customisation menu.     

First Round    
Complete a hole.     

Pure Skill    
Complete a challenge.     

Social Golfer    
Complete a hot-seat multiplayer game.     

Let's See The Goods    
Collect 5 Crates.     

Bat's Your Lot    
Damage 3 bats with one shot.     

Getting The Hang Of It.    
Complete a hole within the course par score or better.     

You Shoot You Score    
Achieve a skill score objective on one of the holes.     

No Task Too Great    
Achieve all the objectives on one hole.     

Rule Britannia    
Complete the Britannia course.     

The Jolly Roger    
Complete the Pirate Cavern course.     

Dead Good    
Complete the Graveyard course.   

6 Secret

Bronze

Show Me The Money    
Collect 20 coins on one hole.     

Tweet Tweet    
Get A Birdie.     

Where's The Prey?    
Get an Eagle.     

That's A Wing Span    
Get an Albatross.     

Fluke or Skill?    
Get a hole in one.     

True Champion    
Complete every objective on all Britannia, Pirate Cavern and Graveyard holes.

http://www.ps3trophies.org/game/worms-crazy-golf/trophies/