There are 28 Trophies that can be collected.

Bronze

Free to Go    
Unlock the "Leave" ending.     

Second Best    
Unlock the "Maria" ending.     

Goodbye    
Unlock the "In Water" ending.

Childhood Trauma    
Defeat Abstract Daddy.     

I Don't Need You Anymore    
Defeat Pyramid Head.     

Where's that Letter!?    
Defeat Flesh Lips.

Fountain of Youth    
Acquire the White Chrism.     

Not So Lost Memories    
Acquire the book of Lost Memories.

Light Reading    
Acquire the book of Crimson Ceremony.

We're Not Alone    
Acquire the Blue Gem.

Silver

Say Your Prayers    
Unlock the "Rebirth" ending.     

It All Makes Sense Now    
Unlock the "Dog" ending.    

Never to be Heard from Again    
Unlock the "UFO" ending.

Overkill    
Acquire the Chainsaw.

Keep Your Distance    
Defeat at least 75 enemies by shooting in SH2.     

Melee Master    
Defeat at least 75 enemies by fighting in SH2.     

Keen Eye    
Find at least 150 items + extra items in SH2.     

Don't Keep Her Waiting    
Complete Boat Stage in less than 1 min 20 seconds.     

Hard to Hit    
Receive less than 500 points of damage in one game, in SH2.

Say Goodbye    
Defeat Mary.     

Restless Dreams    
Unlock the "Born from a Wish" ending.

Unholy Grail    
Acquire the Obsidian Goblet.

Gold

Warp Speed    
Complete SH2 in 3 hours or less.

Who Needs a Gun?    
Acquire the Green Hyper Spray.    

Playing on the Edge    
Complete SH2 with 2 saves or less.

I.Q. Test    
Complete SH2 on Extra Riddle difficulty.

Man's Best Friend    
Acquire the Dog Key.

Platinum

She Would Be Proud    
Unlock all Trophies in SH2.

http://www.ps3trophies.org/game/silent-hill-2-hd/trophies/