15-20 minutes is not a realistic time estimate for this repair. Figure more like 30 minutes to an hour depending on how careful you want to be. You want to be VERY careful. A couple pointers from someone who just did this successfully:
1) The suction cup by itself doesn't work. The pry tool won't help you until you manage to get a connector undone. I used a thumbtack to help pop it open. Not saying you should do this, but that's what I did.
2) DO NOT PULL TOO HARD. You cannot force it and if you do, the display is going to come flying off and you're going to rip the 2 small, ribbon cables holding the display to the backing.
3) The glue holding the battery is a bastard but it will give if you just continuously work around it with the pry tool. Do not actually PRY the battery. Just try to shove it between the housing and the battery so that the adhesive gives.
4) When putting the phone back together, do the top brackets first. If you do the bottom first, the top will bulge and not fit properly.