Get iPad serial number on iCloud
I've found how you do it.

With Xcode installed, open your terminal and run:

open ~/Library/Preferences/com.apple.iPod.plist

This will open the property list editor.

Navigate down to Root -> Devices and look under each device to recognise the one you're looking for. There are 2 identifying factors: DeviceClass (which can be iPod, iPhone or iPad) and Firmware Version String. Through those two I was able to get the serial number I needed.