There are 30 Trophies that can be collected.

Bronze

Hardboiled Seal    
Kill 100 penguins or clones

Disgruntled Worker    
Find 3 Signs

Flight Instructor    
Juggle an enemy for 10 seconds     

Own Medicine    
Kill a helicopter penguin with his own missile

Door Sentry    
Kill 30 Penguins as they step out of a door     

Brainbug Fever    
Brainbug 30 enemies     

High Treason    
Brainbug the penguin above the star in Chapter 6 (Single Player)     

Turncoat    
Kill 20 enemies while brainbugging

Two Birds One Stone    
Kill 2 enemies with one grenade

Bazookin'    
Kill 6 enemies with the bazooka     

Friendly Transit    
Carry the other cooperative player for 500 meters in the same chapter without dying     

For What Reason?    
Launch the silo missile     

Personal Space    
Punch or kick 100 times

Laser Assist    
Kill an enemy by knocking him into a laser door     

Excessive Stacking    
Stack all 3 crates near the end of Chapter 11 (Single Player)     

Hindenburger    
Kill all penguins stationed on the zeppelin in Chapter 3 (Single Player)     

Dirigibully    
Kill all penguins stationed on the small zeppelin in Chapter 8 (Single Player)

Silver

Rebellious Laborer    
Find 20 Signs

Own Pharmacy    
Kill 6 helicopter penguins with their own missiles     

Hydrogen Run    
Escape the large zeppelin with 40 seconds or more on the timer

Too Many Too Soon    
Kill 3 enemies with one grenade

One Shot One Kill    
Kill 10 enemies, each with one gunshot

Big Blimpin'    
Kill all penguins stationed on the big zeppelin in Chapter 8 (Single Player)

Gold

Mission Complete    
Overthrow Putzki and liberate Albatropolis     

Dirty Half-Dozen    
Complete the Cooperative game mode

Hardboiled Orca    
Kill 300 penguins or clones

Revolutionary Fighter    
Find all 45 Signs

Bird Brained    
Brainbug at least one penguin from each of the 7 penguin ranks, including Putzki     

Fear the Spur    
Kill Brno with the knife

Platinum

Platinum Trophy    
Collect all trophies

http://www.ps3trophies.org/game/rocketbirds-hardboiled-chicken/trophies/