I've never had to charge back anyone. Does it make a difference if the money was in my paypal account? Which, I assume, would mean that it never went through a credit card. How would that work? Or is there anything that can be done at all?
If you paid through Paypal using a balance in your Paypal account for the entire amount, then you are at the mercy of Paypal's discretion and have no resources outside of Paypal should you not get any satisfaction with them.
While I have heard many times over from several different sources that Paypal does not review cases involving live animals, I have yet to find any pertinent information on Paypal's site regarding this, probably because they have it so deeply buried.
However, in the 8-9 years that I've been using Paypal, I have never found them very helpful in resolving legitimate and well documented cases I've had with them for the last several years in conjunction with using Ebay.
So, I can imagine that in a situation like this, it's going to be very difficult trying to not only prove your case but also to gain any satisfaction out of it from Paypal. Your best bet when using Paypal is to never keep a monetary balance in their system and always use a credit card when making transactions through Paypal. At least that way you have better protection with a credit card than you ever will with Paypal.
Typically, Paypal will ask you if you received your item. Your answer would be yes. That's one against you. Then they will ask if your item was as described. Well, you can try to argue that the animal first appeared dead due to poor shipping, but it did seem to survive. That would be two against you. You could lie and tell them that it didn't survive the trip, but they might respond with "we don't guarantee live animal arrivals". Then you are still screwed. I don't know of anyway that you could really argue any reasonable point with Paypal, especially since the majority of their claims seem to be used by an automated system.
If you do decide to expend the time and energy to file a claim, keep us updated as to how your proceedings with Paypal go. While I believe that I can safely assume that they will leave you in a much more frustrated way, I would also like to be wrong about them for once.
Good luck!