I've been a tester for four years now so I hope I can help answer your questions.
Being a tester is likely the best way to get into the industry without a degree. Most studios do not require a special degree but the work can be difficult at times. QA commonly does not require prior experience ether, but it is a plus. Some even hire through temp agencies. But something that looks very
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on an application for QA is beta testing. It shows that you have enough of a passion for it, to do it for free.
Some places require some crazy stuff. I think Microsoft wants all of their testers to have software engineering degrees...yeah...to do QA.
To be honest a degree does not make you a
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tester. I'm one of the best testers in my company and I don't have any college degree. We have testers who were highly educated in the field and could not find a bug if it was jumping up in down in front of them.
I just monitored the game company websites and gamasutra. Every time I saw an opening for QA I put in my application. It only took one for me but I would recommend you stick with it. Getting your foot in the door is the most important first step.
PS: A lot of studios do not hire permanent testers. You simply get hired near the end of a game, then get laid off when the game/DLC passes submission.