There are 12 Trophies that can collected.

Bronze

Welcome to Papagaya Island
Kill the miniboss in Puerto Cálao.

Rumble in the Jungle
Defeat something huge.

Get the heck outa here you nerd
Defeat the final boss.

By hook or by Crook
Complete all challenge rooms.

Both guns blazing
Complete the game in coop mode.

TASC Force
As the primary player, complete a level by only finishing off enemies with your bionics.

Stiirike
As the primary player, kill 4 enemies with one barrel.

Silver

Rearmed
As the primary player, obtain all bionic arm upgrades.

Billy Hoyle
As the primary player, complete the game without jumping.

Last Action Hero
As the primary player, complete the game on hard difficulty.

Cap Commando
As the primary player, complete all levels with both prestige upgrades equipped.

Gold

OCD
As the primary player, find all Yasichis.

http://www.ps3trophies.org/game/bionic-commando-rearmed-2/trophies/