That looks like damage caused by a load shift where a heavy package fell onto your package. The best packaging job on the planet won't protect the internal contents of your hatching eggs from a hit like that.
Did you look at the tracking number history of that package and follow its progress? I'm sure it went through the Chicago and Portland hubs, and possibly the Seattle hub as well. It also had a long distance to travel across the country.
I admit for a couple of reasons that I was concerned when
@Nyla shipped hatching eggs to my place in Georgia. First, after working in the shipping business, I don't trust shippers with packages that contain delicate contents. There's a lot of jostling that goes on with the handling of packages. For example, on a number of occasions I have traveled several hours one way for local pick up of hatching eggs, and one time several hours just to pick up a single four-week-old cockerel that we wanted. Second, my local post office makes a lot of shipping and handling errors. At least that has been my experience with them. They don't even have my street spelled correctly in their system. Only in Georgia! Anyway, I was concerned that the hatching-eggs would either be forgotten in some hot room or crushed through carelessness. However, what I learned is that my county is rural enough that the post office has an annex at a second location for livestock shipments and hatching eggs. What a pleasant surprise! They treated our hatching eggs with special care.
As for shipping, I think your best bet is USPS Priority Mail. UPS ground goes through a lot of hubs and handling, and Next-Day Air and 2nd-Day Air are cost prohibitive.
BTW, I see that you're from Oregon. My father was from the other side of the Cascades in Hammond near Astoria, right at the mouth of the Columbia River. It was there while visiting my grandparents on their small farm that I fell in love with chickens. They grew and raised everything that they ate. My dad told me that he had never eaten a canned vegetable until he was 12 when a friend shared a can of beets. Times sure have changed.