Is it possible to Crotchet a Barbarian arm-guard using 550 cord?

It looks like that cord would be a good choice for those arm guards. If the dog's collar is made with the cord you mention, yes, it is a good size to work with. You'll need to buy a honking-big crochet hook to work with it. I strongly recommend taking a strand of 550 cord to a real yarn shop, not a generic crafts supplies store. A real yarn shop is much more likely to have knowledgeable people there. They can tell you which size hook to buy.