Breaking Down Keys
OK, so the key fob is actually only held together with one screw (assuming you just removed the battery tray).
This screw is hidden behind the Fiat badge on your key. You should be able to prize this out very gently with a small flat point screw driver. If you get a stubborn one apply a little heat with hair dryer. They typically remove easily though.
Mine was missing - replacement badges are available on eBay too. i've gone for Abarth badges as it's Abarth car.
After the badge is removed undo the screw that this reveals.
take note in your current key, clipped inside the back (non-button) side of the shell is a small grain of rice sized microchip. This is the immobiliser chip - take great care that it doesn't fall out. If you lose it, you're in a world of pain.
So to split the casing you can just prize it apart with your fingers, it just clips in around the rim. I used a little guitar pick tool as I don't have any finger nails just to pry apart. Be aware the blade is on a spring which may ping if you're not expecting it too.

