How to fix a Nexus 9 that bootloops after an official update?
You should still be able to sideload an official OTA update from the stock recovery. You can get the official OTA images here: https://developers.google.com/android/ota


Download the latest OTA image for the Nexus 9 from that page
Reboot into recovery mode
Press the volume up and power keys at the same time to activate the hidden menu
With the volume keys, highlight “apply update from ADB” and press the power button to choose it
From your computer, execute adb sideload otaFilename.zip