There are 3 encores for each chapter. With 8 chapters this means you need to finish 24 encores. All encores are timed and unlock after finishing the finale in that respective chapter. Some are incredibly easy and others are a real pain. If you are looking to do this the easiest way I would recommend Normal Solo playthrough, but Normal co-op isn't too bad as long as you have a good partner. Insane Solo playthrough would be the next easiest as these are all time trials anyway. Many basically require you to not die at all in order to finish in the time alloted.
I've included some excellent video guides that I take no credit for. They really helped me on some tough levels. All credit goes to the uploader, LinkinX112.
Update:
destinee ehgc mentioned in the comments a tip that can't be called out in the video. In Chapter 8 Encore 3 if you rubber band the right stick so that the camera is looking up it gives you a slightly better view of the projectiles and makes it a bit easier to finish.