I have an iPad 3, running iOS 8.3. I am unable to update it to iOS 9.3.
When checking for Software Update in Settings app, it says that I have the latest version installed.
How do I update it to iOS 9.3.5?
Start by checking the version of iOS currently installed on your iPad by going to Settings app → General → About reading the value for Version.
If the reported version is still iOS 8.3, you can restore your iPad with an image of iOS 9.3.5 which can be downloaded from IPSW.me.
Carry out the instructions below one by one:
Backup your device: Connect to iTunes, select your iPad and perform a local backup of the device.
Download iOS software image: Go to IPSW.me, choose your device, select the image for the latest iOS release (iOS 9.3.5 in your case) and download it. Note that the latest image will be highlighted in Green with Signed IPSWs written on top.