There are 49 Trophies that can be collected.

Bronze

Zombie Hunter    
Defeat 100 zombies.    

Zombie Collector    
Defeat each type of mutant variant.    

Recycler    
Collect 100 items in battle.    

Old-School    
Defeat 10 zombies using wield-able objects.    

Road Rage    
Run over 10 zombies with a forklift or bulldozer.    

Nice Try    
Shoot down an enemy projectile with a Heat Snipe.    

Steamed Vegetable    
Kill a Hermit with fire while it is still armored.    

Oh, the Humanity!    
Successfully Heat Snipe a gas tanker.    

Golden Brown    
Defeat 50 zombies with fire.    

My Eyes!    
Daze 50 zombies with stun grenades.    

Heavily Armed Bank    
Amass over 10 million yen.    

Substory 4    
Finish 4 substories.    

Substory 20    
Finish 20 substories.    

Substory 40    
Finish 40 substories.    
 
Kamurocho Spelunker    
Initiate the Kamurocho Subterranea mission.    

Start of Something Good    
Befriend your first Perfect Partner character.    

Social Butterfly    
Have all 14 partner characters available.    

Mission Complete!    
Clear a directive from Hasegawa.    

Hasegawa's Right Hand    
Cumulative point total from Hasegawa's directives hit 5,000.    

Vigilante Gourmet    
Order from every restaurant at least once.    

Getting Some Action    
Fight zombies together with a hostess.    

My First Mod    
Mod one weapon or piece of armor.    

A Weapon Freak is Born    
Create at least one weapon from each category.    

Official Sponsor    
Fully upgrade Kamiyama's truck.    

All Units, Report!    
Train at Gary's Boot Camp with all four protagonists.    

Life of the Party    
Play every song at karaoke.    

Lounge Lizard    
Play darts and pool five times each.    

Outdoorsman    
Go golfing and fishing once each.    

Indoor Sportsman    
Go batting, bowling, and play table tennis three times each.    

Pro Gambler    
Play each Japanese gambling game once.    

Casino Master    
Play each casino game once.    

Welcome to SEGA    
Play each game in Club SEGA.    

Pachinko Wizard    
Obtain the “trophy” prize at the Volcano Prize Exchange counter.    

Brainiac    
Win at mahjong and shogi once each.

Silver

Akiyama Trophy    
Land 100 head shots with Akiyama.    

Majima Trophy    
Defeat 100 enemies using Heat Sniping with Majima.    

Goda Trophy    
Destroy 100 wield-able objects with Goda.    

Kiryu Trophy    
Defeat 100 mutant variants with Kiryu.

11 Secret

Bronze

Part I Complete    
Complete the four chapters of Part I.    

Part II Complete    
Complete the four chapters of Part II.    

Part III Complete    
Complete the four chapters of Part III.    

Part IV Complete    
Complete the four chapters of Part IV.

Silver

The True Ending    
Complete Extra Hard Mode.

Unsurpassed Power    
Reach the maximum character level.    

Underground Kings    
Clear 50 floors in the Endless Subterranea.

Gold

Thanks for Playing!    
Complete the Final Chapter.

Savior of Kamurocho    
Complete Dead Souls Mode.    

Amon's Vanquisher    
Defeat Amon.

Platinum

Platinum Trophy    
Earn all other trophies in the game.

http://www.ps3trophies.org/game/yakuza-dead-souls/trophies/