There are 17 Trophies that can be collected.

SILVER

Destroyer Destroyer
Sink 5 destroyers in campaign game mode

Carrier Killer
Sink a carrier in campaign game mode

Torpedo Master
Hit a moving ship with a torpedo

Mind the Water
Successfully land on carrier at mission’s end

Ship Sinker
Sink 20 ships in campaign mode

Ace
Shoot down 100 enemy planes in campaign mode

Good Show
Place in top half in multiplayer match with at least 6 players

GOLD

Japanese Campaign
Complete both IJN Campaigns

American Campaign
Complete both USN Campaigns

Torpedo Wizard
Hit a manoeuvring ship with a torpedo

Aces High
Reach maximum experience (255) with any pilot.

Multiplayer Ace
Perform 3 kills in row in MP

Cracking Good Show
Place first in multiplayer match with at least 6 players

Multiplayer Veteran
Play 15 multiplayer matches to the end

USN officer
Win 5 multiplayer matches with USN team

IJN officer
Win 5 multiplayer matches with IJN team

PLATINUM

Platinum
Awarded for successfully collecting all trophies from Air Conflicts: Pacific Carriers

http://www.ps3trophies.org/game/air-conflicts-pacific-carriers/trophies/