You will need another exact same series MacBook air to swap out the SSD with, that is assuming the issue is within the systems logic and not the SSD. If the SSD is failing then that won't help.
As an alternative you could try setting up your MacBook air in target mode and then using a second Mac retrieve the data. Follow this Apple TN: [http://support.apple.com/kb/PH13842|Transfer files between two computers using target disk mode].
To diagnose what is failing here you could pop off the cover and with the battery disconnected, remove the SSD and then try restarting the system without the SSD, but with an external bootable drive. If the system shows the same symptoms you have proven the issue is within the logic board not the SSD.
Frankly, I would just go to Apple and have them repair the system as it should be covered under warranty still.