If you read my guide for the "You Soothed" achievement, the same strategy applies here. Once again, you never have to look at the cameras, except for the one with the music box. Upon starting, check the hallway, left vent, right vent, wind the music box, then the second you drop the camera, quickly press
to drop the mask just in case Withered Bonnie, Chica, Freddy, or Toy Freddy have gotten into your office. If no one is there, lift the mask, check the hallway, then the vents, then wind the music box, then drop the mask once again. Repeat this process. If Withered Foxy is in the hallway, flash the light 7 times, then check the vents. Note that if anyone is in the vents, drop the mask. As soon as they leave, check the hallway once again, then wind the music box. The main thing you need to remember is to drop the mask as soon as you drop the camera. There will be a withered animatronic almost every time, so be careful. I will eventually post my play-through of this night, so be on the lookout.
Edit: Here's my playthrough.