There are 50 trophies that can be earned in this title.

Bronze

Certified UAA Rank 10
Defeat the UAA 10th ranked assassin

Certified UAA Rank 9
Defeat the UAA 9th ranked assassin

Certified UAA Rank 8
Defeat the UAA 8th ranked assassin

Certified UAA Rank 7
Defeat the UAA 7th ranked assassin

Certified UAA Rank 6
Defeat the UAA 6th ranked assassin

Certified UAA Rank 5
Defeat the UAA 5th ranked assassin

Certified UAA Rank 4
Defeat the UAA 4th ranked assassin

Certified UAA Rank 3
Defeat the UAA 3rd ranked assassin

You're trying, 3rd-rate
Earn gold medal on 1 part-time job

Not Bad
Earn gold medal on 5 part-time jobs

You're in my heart's Platinum Hall of Fame
Earn gold medal on all 9 part-time jobs

I guess you're not just 3rd-rate
Get a gold medal on 1 K-entertainment assassination mission

There's still plenty of gigs left
Get a gold medal on 10 K-entertainment assassination missions

Duly ranked up to the top
Get a gold medal on all 20 K-entertainment assassination missions

You wanted a thrill, didn't you?
Get gold medals on 1 free fight missions

Just like Lee in the last minute or not
Get gold medals on 5 free fight missions

I believed in your power
Get gold medals on 10 free fight missions

You've gotten used to killing, huh
Defeat 51 enemies

The association has received a bill for the damages
While riding motorcycle destroy 51 objects

We'll take it out of your winnings, just in case
While riding motorcycle destroy 510 objects

Something new? Wait for the sequel, you Otaku!
Purchase every beam katana and accessory from Dr. Naomi

We're out of business, bro
Purchase every piece of clothing from the AREA 51 shop

Otaku killer's killer fashion ♪
Obtain half of the T-shirts in the game

The Silvia cards are ultra-rare
Collect half of the trading cards in the game

Travis! Your throws are the best!
Learn all wrestling moves

Wow, you've done it. You're reached the end of the path
Learn all techniques from Thunder Ryu

You're a master. Don't hesitate, rush forward
Learn all techniques from Randal Lovikov

Surprisingly sweet? Still, don't underestimate me
Complete the game on BITTER difficulty

Aren't you popular
While playing on Very Sweet Mode watch all five female characters in their new erotic costumes.

The Destroy Warriors want to draft you
Reflect a bullet during Dr. Peace assassination battle

You're almost ready for Hollywood
Block Destroyman's Destroy Beam

He's pretty good at taking punishment
Use your beam katana to reflect a human clone back at Bad Girl

Those clothes… you're such a loser
Dress Travis up like his favorite anime character

You're pretty good
Defeat 30 enemies without any damage

Destroy Super Express Full Throttle!
While using turbo on your motorcycle destroy 51 containers

Did it make you remember the Calgary Hurricanes era?
Execute 10 successful wrestling moves in a row

Did you have sweet dreams?
Defeat all the UAA rank fights without losing only using the Bloodberry katana

Like a master swordsman
Execute 5 successful guard attacks in a row

You surpassed your master?
Ranking stage was cleared without receiving the damage

Why don't you just live in the toilet?
Save at every saving point

You're a magician?
The recovery item was produced from the stick of magic

Silver

Certified UAA Rank 2
Defeat the UAA 2nd ranked assassin

The S stands for Silvia, you know?
Earn an "S" rank on every UAA rank assassination mission

Yes, like that! Keep killing!
Defeat 510 enemies

I want all this season's new releases
Obtain all the T-shirts in the game

Otakus always have to get the complete set, don't they
Collect all the trading cards in the game

Gold

It's a massacre! You're the best, Travis!!
Defeat 5100 enemies

Platinum

Welcome to the Garden of Madness
All trophies were acquired

2 Secret

http://www.ps3trophies.com/forums/trophy-news/41349-no-more-heroes-heroes-paradise-trophy-list.html

The game will also feature PlayStation Move support at launch.