There are 50 Trophies that can be collected.

Bronze

World Domination!
Fight on all maps.

Training All Over Again
Do Training for the first time.

Don't Forget the Basics
Complete Tutorial until the end.

Beginning of a Fantastic Tale
Win 1 Event Battle in Story Mode

Monster on a Full Moon
Clear a Giant Boss Battle in Story Mode for the first time.

Great Air Battle!
Do a Sky Chase in Story Mode for the first time

I'm Going to Change the World!
Win 1 Event Battle in Hero Mode

Your Real Training Starts Here
Clear Hero Mode training for the first time

All 7 Are Here!
Do a Chase Battle in Story Mode for the first time

How Do I Look?
Obtain a Hero hairstyle for the first time

Becoming Fashion Aware
Obtain a Hero costume for the first time

The Martial Artist's Path
Obtain a Hero Fight Style for the first time

Master! Please Teach Me!
Obtain a Hero Master for the first time

Growing in Power
Obtain 500 Hero AP

Point Getter
Obtain 1000 Hero AP

Tapping into Latent Power
Collect 10 Skills

Which One Shall I Choose?
Collect 10 Super Attacks

I Still Want To Fight
Win 5 times in 1P vs. CPU battle.

I Want to Fight Someone Strong!
Win 30 times in 1P vs. CPU battle.

Fight Seeker
Win 50 times in a 1P vs. 'Very Strong' CPU battle.

Defense Learner
Perform Defense Reaction-Guard 10 times total in real battle.

Defense Professional
Perform Defense Reaction-Guard 100 times total in real battle.

Evasion Learner
Perform Defense Reaction-Evade 10 times total in real battle.

Evasion Fiend
Perform Defense Reaction-Evade 100 times total in real battle.

Interception Learner
Perform Defense Reaction-Intercept 10 times total in real battle.

Counter Hero
Perform Defense Reaction-Intercept 100 times total in real battle.

Expert
Successfully perform Clashes 20 times total in real battle.

I See Right Through You!
Successfully perform Clashes 100 times total in real battle.

Moves On Parade
Perform 50 Super Attacks total in real battle.

Master of Moves
Perform 50 Ultimate Attacks total in real battle.

World Tournament Champion
Win the World Tournament.

Cell Games Champion
Win the Cell Games.

Battle Rookie
Fight in an Online Battle 1 time

Regular Battle Customer
Fight in an Online Battle 10 times

Battle Veteran
Fight in an Online Battle 30 times

Title Holder
Collect 5 or more titles.

Silver

The Actors are All in Play!
Unlock all characters and forms.

Goodbye, Dragon World
Clear Story Mode for the first time

Limit Breaker
Obtain 20000 Hero AP

Skill Master
Collect 20 Skills

Super Attack Collector
Collect 30 Super Attacks

W.Tournament True Champion
Champion of World Tournament on Hard Difficulty.

Cell Games True Champion
Champion of Cell Games on Hard Difficulty.

Title King
Collect 30 or more titles.

Gold

I Changed the World!
Clear Hero Mode for the first time

Platinum

OVER 9000!!!!
Obtain all the trophies.

4 Secret

http://www.ps3trophies.com/forums/ps3-trophy-news/4309-dragon-ball-z-ultimate-tenkaichi-trophy-list.html