Would a nucleus composed of multiple nucleons stay stuck together with that much energy? If it's zipping along and not interacting with the anything then sure but how did it get that much energy in the first place?

Yes, while there is a large amount of uncertainty, it is believed they the majority of the highest energy cosmic rays are nuclei of elements like iron. For people like me, in the business of finding high energy neutrinos (I'm not involved in km3net, btw), that's a bad thing since that means the highest energy cosmic rays convert less efficiently into neutrinos when interacting with the cosmic microwave background.

How they got so much energy in the first place is kind of an open question. Generally it involves magnetic fields and shock fronts, getting a little kick each time (but yes, you also have to avoid disintegrating the nucleus in the acceleration environment!)