I was able to finish it, but it took quite a while. Here are 3 techniques that worked for me.
1. Don't bother with the lights unless you're checking if Bonnie or Chica are gone, as their footsteps will tell you when they arrive but not when they leave. Sometimes you don't even need to do that, as I found Chica can go away almost instantly and Bonnie usually takes about 4 seconds, so you can sometimes do it without using them at all.
2. Check pirate cove every 2 or 3 seconds, but only stay on the camera for a split second. If Foxy disappears from camera, wait until you hear the audio cue that tells you they are about to come to the door, and shut it the moment you hear it. Sometimes this can be a problem if someone else comes to the door at that exact moment, in which case I'd advise shutting the door and checking the left hall to trigger the attack.
3. Freddy moves near the end of each hour and laughs when she does so. 5 laughs mean she's in the kitchen, usually getting there just before 5am. While she's there you need to keep the camera on her, even if it's down, and if you do change the camera make sure the right door is shut while you do so. This takes up much more power, but if you've saved enough in the previous hours you should be ok. She will move back to her previous camera not too long before 6am, at which point you no longer need to worry about her.
I was able to complete it after about an hour, and I only did so after running out of power.
Sorry for the length, and the credit for some of these techniques goes to TheUndying, who made a longer guide for how to beat the harder nights. Hope this helps :)