Here is the full list of all 57 Heavy Rain trophies - there are 50 bronze, 4 silver, 2 gold and 1 platinum.
Hassan's Shop - Persuade the Robber to leave
Welcome, Norman! - Remember the time it was at the park and what Shaun was wearing
Father and Son - Follow the schedule with Shaun and put him to bed in a good mood
Prologue - Complete the drawing + Set the table + Play with kids
Shrink and Punches - Do not stop Blake from hitting Dupré
Face to Face - Do not get shot in Kramer's villa
Trapped - Save Lauren underwater
The Old Warehouse - Save the Origami Killer before he falls, with Jayden or Madison
The Rat - Work out where Shaun is held
Find all clues using ARI (Crime scene + Mad Jack + Fish tank) and find the Origami Killer
The Doc - Do not drink the Doc's beverage
The Shark - Do not kill the Drug Dealer
Jayden Blues - Resist Triptocaine
Fugitive - Manage to escape Blake in the subway station
Nathaniel - Shoot Nathaniel
Lexington Station - Knock down at least 50 passers-by
Crime Scene - Find all clues related to the Origami Killer in the scene
Sleazy Place - Beat Troy
Finish HEAVY RAIN™
Complete the story with four characters alive
Save Shaun
Killer's Place - Survive the explosion by hiding in the fridge
Succeeded in all Ethan's trials
The Rat - Drink the poison
Face to Face - Give Kramer his medicine
On the Loose - Escape the police at the motel
On the Loose - Forgive Madison
Sexy Girl - Take off no more than one item of clothing during the strip-tease
Eureka - Prepare a good omelette on time
Mad Jack - Survive the fights against Mad Jack
The Doc - Escape before the Doc returns
The Shark - Kill the Drug Dealer
Under Arrest - Switch the camera off in the surveillance room before saving Ethan
Jayden Blues - Play the piano without a wrong note
Fugitive or On the Loose - Get arrested by Blake
The Lizard - Cut your finger using saw or scissors
Shrink and Punches - Stop Blake from hitting Dupre
The Butterfly - Complete the Butterfly Trial successfully
Kramer's Party - Defeat Gordi's bodyguards
Covered Market - Beat Korda in the cold storage
The Bear - Complete the Bear Trial successfully
Nathaniel - Do not shoot Nathaniel
Lexington Station - Find the correct locker on first try
Paparazzi - Leave home without being spotted by the journalists
The Park - Play two games with Shaun successfully and buy him candy
Sleazy Place - Lead Lauren to talk about her son
Thank you for supporting Interactive Drama
Unlock all trophies
Suicide Baby - Make no mistakes taking care of the baby
The Bear - Take the best route on the highway
The Butterfly - Give up or fail the Butterfly Trial
The Lizard - Cut your finger using axe, knife or pliers + disinfect or cauterize the wound
Twins - Follow your brother without making any mistakes
On the Loose - Do not forgive Madison
The Old Warehouse - Reach the end with all characters... and fail
Clean Manfred's shop of evidence + Let Lauren, Hassan and Kramer die + Kill Madison and Jayden + Origami Killer free
See all endings