Before starting, make sure your Macbook is fully powered off and unplugged from any power source. It's wise to work on a non-conductive surface to prevent static electricity damage and wear anti-static wristbands to protect sensitive components.
This tutorial will guide you in detail how to remove the Apple A1322 / MacBook Pro 13" A1278 battery. You can watch the tutorial video below.
Step 1
Remove the 10 screws securing the rear case of the MacBook Pro 13" Unibody.
Step 2
Gently lift the lower case and push it toward the back of the computer to release the tabs.
Step 3
Remove the tri-point screws securing the battery to the upper case.
Step 4
Use the flat end of a spudger to disconnect the battery connector from its socket on the logic board.
Step 5
Remove the battery from the upper case.