There are 35 Trophies that can be collected.

Bronze

DIPLOMATIC
Perform a hostage trade.

EAGLE EYES
Point out a special enemy using the ‘shout out’ command.

CHENEY?
Defeat a Bulldozer with a shotgun.

INTIMIDATING
Get a Heavy SWAT to give up.

LEFT FOR DEAD
Finish a heist in custody while all your team mates are alive.

LAST MAN STANDING
Beat a heist after having been the only one alive.

BLOOD IN, BLOOD OUT
Trade all the butchers in SLAUGHTERHOUSE

DODGE THIS!
Beat a heist on normal difficulty or above, having killed a Bulldozer without taking damage from any Bulldozer

A BRIDGE TOO FAR!
Complete the GREEN BRIDGE on hard or OVERKILL difficulty.

BUT HOW?
Get the armored car to drop without shooting at it in SLAUGHTERHOUSE.

WINDOWLICKER
Defeat a law enforcer planting C4 in FIRST WORLD BANK on hard difficulty or above.

CIVIL DISOBEDIENCE
On GREEN BRIDGE, destroy all the lights in the main scaffolding tower.

ARE THERE MORE THAN TWO?
Find ten money bundles in PANIC ROOM.

DARKNESS
On GREEN BRIDGE, destroy all the lights in the main scaffolding tower

YOU CAN RUN BUT YOU CAN’T HIDE
In PANIC ROOM, take the key from Chavez within the first 45 seconds of starting the mission

SHINOBI
Bypassing all 3 consoles before raising the alarm, beat DIAMOND HEIST on hard or OVERKILL difficulty

I AIN’T AFRAID NO MORE
Gain a level in the Assault tree during an assault.

CRACK-BANG
Gain a level in the Sharpshooter tree with your last kill being a Sniper.

Silver

LAY ON HANDS
Gain a level in the Support tree while reviving a teammate.

ARE THOSE THE BLUE ONES?
Steal all the sapphires in DIAMOND HEIST on hard or OVERKILL difficulty

GOLD DIGGER
Beat SLAUGHTERHOUSE within 15 minutes, taking all the gold.

STAND TOGETHER
Beat HEAT STREET on normal difficulty or above without anyone getting downed

QUICK DRAW
In PANIC ROOM, kill all armed thugs in and around the apartment building within 60 seconds of you and your crew drawing your weapons

NO PHOTOS
Destroy all the cameras in FIRST WORLD BANK within 10 seconds of drawing your weapons.

HOT LAVA
Don’t let any law enforcers reach the graffiti on the center of the roof in PANIC ROOM from the SECURE THE ROOF objective until the ESCAPE objective on hard or OVERKILL difficulty.

FEDERAL CRIME
Defeat 25 FBI agents in a row.

ONE SHOT, ONE KILL – REPEAT
Get 30 kills using 30 shots, using only the M308 Rifle.

BOMB MAN
In DIAMOND HEIST, defeat all twelve Patrol Guards using only trip mines.

ARE YOU READY YET?
In DIAMOND HEIST, get Bain to come back for you at least 7 times.

Gold

EASY STREET
Beat HEAT STREET on OVERKILL difficulty, with your group accuracy being at 60% or higher

I PUSHED THE BUTTON AND LIVED!
In DIAMOND HEIST, get the big diamond and escape on OVERKILL difficulty with you and all your team mates alive

NOOB HERDER
Beat any heist on OVERKILL difficulty with three other players who are all using the Noob Lube perk.

DON’T LOSE FACE
Beat all heists on OVERKILL difficulty without anyone getting traded from custody

PAYDAY
Acquire one billion dollars in total cash.

Platinum

OVERKILL
Do it all.

http://www.ps3trophies.org/game/payday-the-heist/trophies/