If any of the adhesive strips broke off and the battery remains stuck to the rear case, prepare an iOpener or use a hair dryer to heat the rear case directly behind the battery. This will help soften the adhesive.
Flip the iPhone back over and thread a strong piece of string (such as dental floss or a length of thin guitar string) underneath the battery.
Pull the string from side to side in a sawing motion all along the length of the battery to separate the adhesive. This can take some time since the adhesive is slow to deform, but with patience it will come free. Do not deform or damage the battery.