Hello, Owen.
Thank you for visiting Apple Support Communities.
Here is the best troubleshooting article to go through when experiencing issues updating your iOS device over-the-air.
Resolve issues with an over-the-air iOS update
http://support.apple.com/kb/TS4431
You can also update this iPad via iTunes on a computer as an alternative.
If you can’t update wirelessly, or if you want to update with iTunes, follow these steps:
- If you use your device's Personal Hotspot for your computer's Internet connection, update your device wirelessly or connect your computer to another network.
- Install the latest version of iTunes on your computer.
- Plug in your device to your computer.
- In iTunes, select your device.
- In the Summary pane, click Check for Update.
- Click Download and Update.
If you see an error message while updating your device, you can learn how to resolve iOS update errors in iTunes.
Update your iPhone, iPad, or iPod touch
http://support.apple.com/kb/HT4623
Cheers,
Jason H.