I have seen and tried may of the proposed methods.
-Using Cloud -Using USB -Switching User at title screen -Re-downloading beta -Spamming A button at title screen -ETC
Seeing various people give their success stories I have come to a conclusion. Either these methods may possible increase your chances of the beta working or they mean nothing. I am leaning towards the latter, I think these are coincidences.
The one thing that I am fairly certain that does work is the most basic. Keep trying.
I have tried many, many times today to no avail. Literally just as I was about to make a post about nothing working, it worked. For those getting the critical error problem, I think it's just a matter of being lucky and signing in at the right time.
If you want to get in just keep trying. It took me many ties. I am of the belief that everyone can get in however its just a matter of how many times it will take. Some get in after 5 tires some get get after 50. You can keep trying or you can wait until Trion does something to fix it.
http://i41.tinypic.com/1609a9h.gif "If you can eat your food while everyone else is losing theirs and blaming you, you straight, homie." -Big Smoke