There are 51 Trophies that can be collected.

Bronze

World Domination, Go!    
You started the game. Great work!    
 
Mugen Field: Access    
Entered the Mugen Field for the first time.    

Mugen Field: 50th Floor    
Reached the 50th floor of the Mugen Field.    

Mugen Field: 100th Floor    
Reached the 100th floor of the Mugen Field.    

Shampuru Revolution!    
Be a victim of your own Peon Ball.    

G-Castle Battler    
Won a G-Castle battle.    

10,000 Damage!    
Dealt 10,000 points of damage.    

100,000 Damage!    
Dealt 100,000 points of damage.    

1,000,000 Damage!    
Dealt 1,000,000 points of damage.    

10,000,000 Damage!    
Dealt 10,000,000 points of damage.    

100,000,000 Damage!    
Dealt 100,000,000 points of damage.    

Signed, Sealed, and Delivered!    
Won a battle in the Mugen Field with all commands sealed.    

Assault Those Baddies!    
Successfully get a preemptive attack.    

Continental Peon    
Turn a continent into your peon.    

Moe Kill First-Timer    
Successfully make an enemy your peon.    

Nice Combo!    
Performed a combo with at least 100 hits.    

Fantastic Combo!    
Performed a combo with at least 999 hits.     

Nice TCS!    
Activated a Triple Counter Stop.    

Fantastic TCS!    
Activated a Triple Counter Stop at full power.    

Take a Dip!    
Checked out the stat-boosting hot spring for the first time.    

Level 999    
Reached Level 999.    

Fusion Complete?    
Used Peon Fusion over 10 times.    

It Flew?!    
Performed a Blast Off attack.    

Deep Space Flight! Go!    
Performed a Blast Off attack at maximum power.    

Air Superiority!    
Destroyed an object in the air.    

Job Master    
Unlocked all Jobs.    

Overwhelming Millionare!    
Held more than 100,000,000 G.

Silver

Overwhelming Grind!    
Obtained more than 999,999,999 Mugen Points.    

The God of Moe   
Increased Chou-Chou's Charm Level beyond the 50 percent mark.

Gold

10,000,000,000 Damage!    
Dealt 10,000,000,000 points of damage.    

The Goddess Has Descended?    
Increased Chou-Chou's Charm Level to 100 percent.    

Overwhelming Peon Ball, GO!    
Made a Peon Ball over 10,000,000,000 Km in size.

19 Secret

Bronze

Sun World Conquered!     
Made the hero and demon lord of Sun World into your peons!    

Moon World Conquered!     
Made the hero and demon lord of Moon World into your peons!    

Fire World Conquered!     
Made the hero and demon lord of Fire World into your peons!    

Water World Conquered!     
Made the hero and demon lord of Water World into your peons!    

Tree World Conquered!     
Made the hero and demon lord of Tree World into your peons!    

Metal World Conquered!     
Made the hero and demon lord of Metal World into your peons!    

Seven World Conqueror     
The seven worlds are all yours now!    

The End?     
Saw the normal ending.    

The Real End!     
Saw the true ending.    

Shampuru Fan     
Obtained more than 20 types of shampurus.    

Shampuru Collector     
Obtained more than 50 types of shampurus.    

G-Castle Master     
Learned all G-Castle skills.    

Fever Time! Go, Go, Go!     
Activated Fever Mode.    

Level 9999     
Reached Level 9999.    

Hard Worker    
Unlocked a hidden Job.

Silver

Doppelganger Case: Closed!     
Defeated all the doppelgangers.    

Sun Goddess Supernova!     
Defeated the Sun Goddess.    

Master Chou-Chou     
Obtained all types of shampurus.

Platinum

The Undisputed God     
Unlocked all trophies. Are you an undisputed god now, too!?

http://www.ps3trophies.org/game/mugen-souls/trophies/