Welcome to iMore! Have you done a hard reset?
Hold the top or side power/sleep button and the home button at the same time until the Apple logo appears, then release.
If that doesn't work, you may need to restore your phone as new. Not from a back up.
Try and delete cache where you can. The app, Battery Doctor, does a good job. Some apps have a delete cache option. Some, like Facebook, you just sign out of, then back in. Others you delete, then reinstall.