Well, I know as an egg seller I don't like it when I get blamed for what the post office does to my eggs. I package them as carefully as I can and make sure they are snug and do my best to make sure they can get to their destination safely. But once I turn them over to the post office it is literally out of my hands. There is nothing I can do from that point on to make sure they reach their destination safe.
Also, it would be your responsibility to open the claim with the post office, since you are the one that would be receiving the money for the compensation. The seller did also put in the listing that this was a possibility, it sounds like from what you're saying in your post, so you knew when you bid on them that this could happen. It sounds like the seller isn't handling it well, and I certainly would have been more apologetic if these were my eggs and I probably would have offered to send more, but it sounds like her packaging was fine since none broke and this really was just a case of the post office doing something to the box that was way out of their control.
By opening a claim you are asking the seller to pay for probably the shipping I imagine, which is money right out of their pocket, and also to forfeit all the money they spent taking care of those birds to get them to lay those eggs that they sold probably in an effort to recoup some costs of taking care of the birds. Not trying to make you feel bad, just trying to show what the seller's perspective is.
Also, I'm not sure that you'll win your claim. It sounds like the seller sent you the eggs you were promised, packed them as best as they could, and put right in their listing that they are not responsible for what the post office does to the eggs after they ship them, which means you were aware that this could happen and agreed to it when you bid. Or at least that's what it'll look like to anyone who reviews the claim.
But yes, the seller is handling this poorly. I would have been really apologetic had these been my eggs and probably offered to ship more for the cost of shipping, but I would't have opened a claim with the post office for my buyer, that would be the buyer's responsibility.
Also, you might try putting them in the incubator. You might be surprised. I just had a shipment go to Hawaii thanks to a post office mess up before it reached me. All the eggs but one, even though they took a weeklong detour to the state that is the farthest away from mine possible and crossed an ocean, and the box got a nice big dent in it on the corner like yours in the process, developed.