iPad air2 shuts off when battery at 66%

Before proceeding with the battery replacement, ensure that you have created either an iCloud or iTunes backup - as the replacement process will cause all locally stored to be lost from the iPad. After the battery has been replaced, you can restore from the backup.

How to back up your iPhone, iPad, and iPod touch - Apple Support

Restore your iPhone, iPad, or iPod touch from a backup - Apple Support

As described your battery may require replacement. Assuming that the iPad remains functional, you would be well advised to directly contact Apple Support - and request a remote battery test. The result of the test may better inform your next steps.

You will find the Contact Support link at top-right of this page. Alternatively, you can open a support case using the excellent Apple Support App. If not already installed on your iPad, the App can be downloaded from the App Store:

https://apps.apple.com/gb/app/apple-support/id1130498044

As a further alternative, you might visit the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP) - where the technicians will be able to test and assess you iPad:

Genius Bar Reservation and Apple Support Options - Apple