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