Fixing the cracked plastic outer shell of an Anvil ATA flight case?

Looks like a stress cracks.
Without replacement of that panel, attempted repairs will likely make it worse.

 

It won't look pretty, but you could patch those over with the same fiberglass & epoxy they use for fixing Corvettes & surfboards.
It's just a fiberglass patch tape that you glue on with epoxy.
As mentioned, it won't be pretty, but it will save the structure of it from cracking further:



Rock & Roll over it with some stickers when it's dry:

 

for that roadworn look
As Seen on TV® Flex Repair Tape - Black