Here is the full list of all 46 Saw achievements.
Stomped five Minions to Death
Unlock 20 locked doors.
Kill 20 Minions
Used 20 Health Syringes
Kill 10 Minions
Unlock 5 locked doors
Complete game using Truth door
Complete game using Freedom door
Kill the Pighead
Release Jeff from his Trap
Five kills with a Table Leg
First kill with a Molotov
Five kills with a Hatchet
Release Obi from his Trap
First kill with an Explosive Mine
Idle for five minutes
Release Oswald from his Trap
First kill with a Scissors
First kill with a Gas Mine
Release Melissa from her Trap
First kill with a Stun Mine
First kill with a Shovel
Stomped first Minion to Death
First kill with a Gun
Release Jennings from his Trap
First kill with a Crutch
First kill with a Syringe
Five kills with a Nail Bat
Four kills with a Bat
Five kills with a Table Lamp
Five kills with a Mop Handle
Died three times
Five kills with a Mannequin Arm
Killed a Collared Minion with a collar detonation
Release Amanda from her Trap
First kill with a Scalpel
Unlocked First Door
Find your first Patient File
Used Health Syringe for the first time
Kill first Minion
Five kills with a Pipe
Fought first NPC
Unlock First Container
Find your first Asylum File
First encounter with Pighead
Complete Reverse Bear Trap