There are 22 Trophies that can be collected.

Bronze

I'm Normal I Promise    
Unlock the "Normal" ending.

Wall Basher    
Acquire the Silencer.

Silver

It Was All in Your Head    
Unlock the "Possessed" ending.

There's a New Sheriff in Town    
Acquire the Beam Saber.     

Flame On    
Acquire the Flamethrower.     

What the Hill Just Happened?    
Acquire the Gold and Silver pipes.

Pest Control    
Defeat Split Worm in under 2 minutes.     

Eye For an Eye    
Defeat Missionary in under 2 minutes.     

A Time to Kill    
Defeat Leonard in under 3 minutes.     

Lost Memory    
Defeat Memory of Alessa in under 3 minutes.     

Blasphemy    
Defeat God in under 8 minutes.     

This Isn't an FPS!    
Defeat at least 75 enemies by shooting in SH3.     

They Look like Monsters to You?    
Defeat at least 75 enemies by fighting in SH3.     

Hoarder    
Pick up at least 100 items in SH3.     

Ninja    
Receive less than 500 points of damage in one game, in SH3.

Gold

Coolest. Dad. Ever.    
Unlock the "UFO" ending.     

Adrenaline Junkie    
Complete SH3 in 3 hours or less.

Makes My Head Hurt    
Complete SH3 with 2 saves or less.     

If Looks Could Kill    
Unlock the Heather Beam.     

Where's Luna?    
Equip the "Princess Heart" costume.     

Heather's Got a Gun    
Acquire the Unlimited Submachine Gun.

Platinum

I Guess it's Time to Roll the Credits    
Unlock all Trophies in SH3.

http://www.ps3trophies.org/game/silent-hill-3-hd/trophies/