I am considering a relo to Portugal, Mexico or Costa Rica from USA
Sorry, I have no experience in moving with birds.
I will say that Portugal will likely be the most difficult as it is in Europe and importing birds can be quite strict, though I believe
@Icey moved from USA to UK with her birds.
I would think that Mexico would be the easiest of the three, but I have no idea, just a guess.
When thinking of moving to another country with your birds, remember to consider whether you think you will settle there or want to move on later.
Going to Portugal would mean moving to another EU country after would not be as difficult.
edit;
forgot to add, to check the CITES list to be sure your bird is not restricted/prohibited.