Replacing the battery in the MacBook Pro 13″ (A1278) shouldn’t be a saga, but there is a trap for beginners!
MacBook Pro 13″ A1278 (2009 Version) uses an Apple A1322 battery NOT the A1278 Battery which is used in the Apple MacBook 13″ Aluminum Unibody Series (2008 Version). If you call most suppliers and ask for a battery for an A1322 MacBook you will be sent an A1322 battery as the A1322 is not listed as customer replaceable (even from Mac sales locations) .
Have we got that? The 2009 version A1278 doesn’t use the A1278 battery. If the base of your 13″ MacBook A1278 is a single piece you need an A1322 battery, if your mac base comes apart (as in the image below) you use the A1278 battery.