Saw

As far as I know, this only includes doors which you walk through, not the locked cabinets. Unlocking the doors requires you to solve a simple puzzle. You will see 6 dials that can be turned by pressing A. You must turn each dial until both sides of each one corresponds to the adjacent dial. It is fairly simple, and you will figure it out eventually through trial and error. In order to pick a lock, you need to have a nail, which can be found by searching many of the cabinets, lockers, and desks in the game. Unlock 5 of these bad boys and the achievement is yours.

If you are really struggling but you have one lock worked out - just die and reload the checkpoint, as they all stack up. You might as well do this for the 20 locks if you've got 15 mins.