There are 34 Trophies that can be collected.

Bronze

Overhead view-just like old times…
Used overhead view on Shadow Moses Island

That Tune Is His Mind Control Music
Played Oishii Two-han Seikatsu and made one of the BB Corps dance

Drum Can Addict
Knocked an enemy soldier flying using a Drum Can

Hurt me more!
Shocked an enemy soldier using Mk. II/III

Emotion Control
Controlled an enemy soldier's emotions using an Emotive Magazine

Hands Up!
Held an enemy soldier at gunpoint and performed a body check

Divine Wind
Caused a "divine wind" using the Tanegashima

You enjoy all the killing, that's why
Killed many enemies in one area, and vomited

Silver

You're pretty good
Got kissed by Ocelot during the final battle

Are you an Otaku too?
Viewed all model posters

Can you feel my power now!!!?
Took control of an enemy soldier's body using the Mantis Doll or Sorrow Doll

FaceCamo Addict
Obtained 10 or more types of FaceCamo (excluding types obtained via password)

Ghost Photography Addict
Snapped at least 5 shots of ghosts on Shadow Moses Island

Where I Can See Ya
Located enemy soldiers using the Scanning Plug

I Just Don't Fear Death
Caused ALERT status while wearing the Corpse Camo

SUNLIGHT!
Obtained the Solar Gun

Gold

I am THE expert on weapons, equipment and cutting-edge technology
Obtained all weapons (excluding weapons obtained via password)

Sounds of the Battlefield
Obtained all iPod tracks (excluding tracks obtained via password)

Flashback Mania
Viewed all flashbacks

Platinum

The Legendary Hero
Obtained all trophies

14 Secret

Bronze

Liquid Sun    
Cleared Act 1 (Middle East).   

Solid Sun    
Cleared Act 2 (South America).   

Third Sun    
Cleared Act 3 (Eastern Europe).   

Twin Suns    
Cleared Act 4 (Shadow Moses).   

Old Sun    
Cleared Act 5 (Outer Haven).   

Laughing Octopus Doll    
Defeated Laughing Octopus by non-lethal means, and obtained the Laughing Octopus Doll.   

Frog Soldier Doll    
Escaped the Haven Troopers in the Middle East by non-lethal means, and obtained the Frog Soldier Doll.   

Raging Raven Doll    
Defeated Raging Raven by non-lethal means, and obtained the Raging Raven Doll.   

Crying Wolf Doll    
Defeated Crying Wolf by non-lethal means, and obtained the Crying Wolf Doll.   

Screaming Mantis Doll    
Defeated Screaming Mantis by non-lethal means, and obtained the Screaming Mantis Doll.

Handle with Caution    
Broke off the most important part of a statue.

LIQUID!    
Piloted Metal Gear REX and screamed at your enemy.

Silver

Crop Circle    
Found a crop circle and heard a mysterious voice.

Gold

Infinite ammo.    
Obtained the Bandanna.   

Stealth Camouflage    
Obtained the Stealth Camouflage.

http://www.ps3trophies.com/forums/playstation-trophy-news/20479-metal-gear-solid-4-trophy-list.html

wolf-OF-chaos said
I thought there was 36 trophies not 20?

34 forgot to put the secret ones at the bottom