There are 51 Trophies that can be earned in this title.

Bronze

Just like Dad would have done
Complete the game on any difficulty level

Shad-owned
Perform a silent kill with Shadow

That's what you gets!
Kill an enemy by knocking or throwing him off a ledge

Got your GAC
Take a GAC hostage

Get ready for a surprise!
Leap over and kick an enemy from cover

Dog tag
Perform a tag team kill with Shadow

Head Banger
Open 10 doors with a hostage head

Scrotality
Perform a Shadow groin takedown

Crime and punishment
Perform 50 takedowns

Dog's dinner
Perform 50 Shadow kills

Bring a gun to a fist fight
Perform 50 disarms

It's all in the timing
Perform 50 counters

Featherweight
Perform 200 3-hit combos

Shadowboxing
Dash evade 50 strikes

The price of justice
Collect 25 cop badges

Medal of merit
Bronze rating on every level

Boom!
Get 30 headshots in any level, on OFFICER or greater difficulty.

Silver

Best cop this city's ever had
Complete the game on OFFICER difficulty

Brawler
Complete any level (excluding the Prologue) without firing a shot

Heavyweight
Perform 100 5-hit combos

Honor the dead
Collect 50 cop badges

Medal of bravery
Silver rating on every level

Shhhhh
Complete any level with 10 silent kills, on OFFICER or greater difficulty.

Perfect balance
Achieve maximum VARIATION BONUS on any level (excluding the Prologue)

Got your back
Complete a level without Jack or Shadow dying (levels 3-10)

First at the scene
Achieve maximum CLEAR TIME BONUS on any level (excluding the Prologue)

Finish him Shadow!
Combine Jack and Shadow to kill 20 enemies in any level, on OFFICER or greater difficulty.

Gold

Retribution
Complete the game on DETECTIVE difficulty

Medal of valor
Gold rating on every level

Platinum

Platinum Trophy
Collect all the game's Trophies

21 Secret

http://www.ps3trophies.org/game/dead-to-rights-retribution/trophies/