Here is the full list of all 46 Saw achievements worth 1,000 gamerscore. It takes around 8-10 hours to unlock all of the achievements on Xbox 360.
Complete game using Truth Door.
Complete game using Freedom Door.
Kill the Pighead.
Release Jeff from his Trap.
First kill with a Shovel.
First kill with a Hatchet.
Release Obi from his Trap.
First kill with fire
First kill with a Mannequin Arm.
First kill with Scissors.
Release Oswald from his Trap.
First kill with an Explosive Mine.
First kill with a Gas Mine.
Release Melissa from her Trap.
First kill with a Stun Mine.
First kill with a Gun.
First kill with a Bat.
First kill with a Nail Bat.
First kill with a Syringe.
First kill with a Table Leg.
First kill with a Mop Handle.
First kill with a Table Lamp.
First kill with a Scalpel.
Release Jennings from his Trap.
First kill with a Crutch.
Killed a Collared Minion with a collar detonation.
Release Amanda from her Trap.
Unlock 20 locked doors.
Used 20 Health Syringes.
Unlock 5 locked doors.
Kill 20 minions.
Stomped five Minions to death.
Kill 10 minions.
Stomped first Minion to death.
Idle for five minutes.
Died once.
Unlocked first door.
Find your first Patient File.
First kill with a Pipe.
Kill first minion.
Fought first NPC.
Find your first Asylum File.
First encounter with Pighead.
Used Health Syringe for the first time
Unlock first container.
Complete Reverse Bear Trap.