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 (Single Player)

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

Putzki Monologues
Find all four episodes of Putzki on TV in a single playthrough

For What Reason?
Launch the silo missile

Method Acting
Kill yourself as an Elite Penguin on Palace TV in Chapter 13

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 Labourer
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

Riding the Thunderbolt
Kill Mega-Brno in Hardboiled mode

PLATINUM

Platinum Trophy
Collect all trophies

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

do you have the PS3 version as well?