Here is the full list of all 56 Heavy Rain achievements. It takes around 25-30 hours to unlock all of the achievements on Windows.
The Bear - Take the best route on the highway
Welcome, Norman! - Remember the time it was at the park and what Shaun was wearing
Hassan's Shop - Persuade the Robber to leave
See all endings
On the Loose - Do not forgive Madison
The Old Warehouse - Reach the end with all characters... and fail
Complete the story with four characters alive
The Rat - Work out where Shaun is held
The Old Warehouse - Save the Origami Killer before he falls, with Jayden or Madison
Clean Manfred's shop of evidence + Let Lauren, Hassan and Kramer die + Kill Madison and Jayden + Origami Killer free
The Rat - Drink the poison
Succeeded in all Ethan's trials
Face to Face - Do not get shot in Kramer's villa
On the Loose - Forgive Madison
On the Loose - Escape the police at the motel
Twins - Follow your brother without making any mistakes
Mad Jack - Survive the fights against Mad Jack
The Doc - Escape before the Doc returns
The Shark - Kill the Drug Dealer
Jayden Blues - Play the piano without a wrong note
Jayden Blues - Resist Triptocaine
Fugitive - Manage to escape Blake in the subway station
The Lizard - Cut your finger using axe, knife or pliers + disinfect or cauterize the wound
The Lizard - Cut your finger using saw or scissors
Shrink and Punches - Do not stop Blake from hitting Dupré
The Butterfly - Give up or fail the Butterfly Trial
Suicide Baby - Make no mistakes taking care of the baby
Nathaniel - Shoot Nathaniel
Paparazzi - Leave home without being spotted by the journalists
Lexington Station - Knock down at least 50 passers-by
Finish HEAVY RAIN™
Save Shaun
Killer's Place - Survive the explosion by hiding in the fridge
Find all clues using ARI (Crime scene + Mad Jack + Fish tank) and find the Origami Killer
Face to Face - Give Kramer his medicine
Trapped - Save Lauren underwater
Sexy Girl - Take off no more than one item of clothing during the strip-tease
Eureka - Prepare a good omelette on time
The Doc - Do not drink the Doc's beverage
The Shark - Do not kill the Drug Dealer
Under Arrest - Switch the camera off in the surveillance room before saving Ethan
Fugitive or On the Loose - Get arrested by Blake
Shrink and Punches - Stop Blake from hitting Dupré
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
The Park - Play two games with Shaun successfully and buy him candy
Crime Scene - Find all clues related to the Origami Killer in the scene
Sleazy Place - Beat Troy
Sleazy Place - Lead Lauren to talk about her son
Thank you for supporting Interactive Drama
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