There are 42 Trophies that can be collected.

Bronze

Up Close & Personal – Brutal Melee another player
Used the Brutal Melee move against another player

Team Player – Play a match as part of a squad
Joined and complete a match as part of a squad

Medic! – Revive another player
Revived a friendly player for the first time

Handy Man – Repair an object
Repaired an object for the first time

Now You See Me – Kill using Cloak
Killed another player while cloaked

Spy Game – Kill using Disguise
Killed another player while disguised

Turf War – Capture a Tactical Spawn Area
Captured a Tactical Spawn Area for the first time

Brutal Footsteps -Silent killing
With the Silent Footsteps skill active, Brutal Melee an enemy player

Highly Decorated – Unlock Ribbons
Unlock all Ribbons in a single match while playing Operations or Warzone

No Go For Launch – Deactivate missile launch
Deactivate the missile launch while playing in Lente Missile Base

Exhausted – Get killed by missiles
Get killed by the exhaust from the missile launch while playing in Lente Missile Base

Bullet Spam – Kill with the Minigun pickup
Get 5 kills with the Minigun pickup in a single match while playing in Mobile Factory

Mini-Gone – Kill a player with the Minigun
Kill any player that is using the Minigun pickupin Mobile Factory

Radec's Revenge – Kill the ISA
Kill 5 different ISA players in a single match while playing in Radec Academy

Turn Back Time – VC9 Missile Launcher kill
Get a single VC9 Missile Launcher kill in Radec Academy

Jetpack on Jetpack Action – Jetpack killer
While flying mid-air, shoot down and kill another flying Jetpack player in Tharsis Depot

Frequent Flyer – Fly for 60 seconds
With a Jetpack equipped, fly for 60 seconds or more in Tharsis Depot

Hacker – Hack Turrets
As an Engineer, successfully hack 3 enemy turrets in a single match

Tag. You're It. – Kill using the Recon ability
Kill 3 enemies within a single activation of the Recon ability while playing as a Tactician

Cloak and Fragger – Kill the Marksmen
While playing as a Marksman, kill 5 enemy Marksmen in a single match

Taken from behind – Brutal Melee from behind
Brutal Melee 3 enemy players from behind while disguised in a single match while playing as an Infiltrator

Immortal – Survive bleedout
With the Field Medic Triage++ ability active, survive bleedout 5 times in a single match

Silver

Demolitionist – Destroy objectives
Demolish both buildings by winning Search and Destroy as ISA and Helghast in Salamun Market

Tactical Mastery – Help capture Tactical Spawn Areas
Be playing at the moment your faction secures all four Tactical Spawn Areas simultaneously in Salamun Market

Death by Proxies – Proximity Mine kills
Using Proximity Mines, kill two enemies within one minute in Blood Gracht

Blood Streak – Kill streak
Get a 5 kill streak in Blood Gracht

Little Big Weapons – Kill with secondary weapons
Get 15 kills using secondary weapons in a single match

Automata For The People – Automata destruction
Destroy an enemy Sentry Turret, Sentry Drone and Medi-Droid in the same match

Jetpack on Exo Action – Destroy Exoskeleton
Destroy an enemy Exoskeleton with your Jetpack while in flight in The Junkyard

Exo on Jetpack – Kill a Jetpack
Kill a flying enemy Jetpack with an Exoskeleton in The Junkyard

Deadly Threesome – Triple kill
Get a triple kill while playing Stahl Arms

I See You – Minigun a Marksman
Kill a Marksman with the Mounted Minigun in Stahl Arms

5 for 5 – Lots of guns
Kill 5 enemies with 5 different primary, secondary or explosive weapons in a single match

Jack of All Trades – Kill all careers
Kill one enemy of each career type in a single match

Career Minded I – Rank up
Reach the rank of Lieutenant I

Wasting Away I – Kill enemies
Kill a total of 500 enemy players online

Gold

Grand Slam – Win a match in 3 multiplayer modes
Won a match in Operations, Warzone & Guerrilla Warfare modes

Career Minded II – Rank up
Reach the rank of Lieutenant I

Wasting Away II – Kill enemies
Kill a total of 1000 enemy players online

Platinum

Platinum
Collect all Killzone 3 Multiplayer Trophies

2 Secret

http://www.ps3trophies.com/forums/playstation-trophy-news/12925-killzone-3-multiplayer-trophy-list.html

Origami Killer said:

Is there going to be an update for Killzone 3 (full game) which allows us to get these trophies? 

doubt we will get them in the main game mate.