火による判断 would mean "a judgement by fire", but I have no idea if it represents what you mean by "trial by fire" at all. I think my translation means both a judgement handed out BY fire, and a judgement enacted through fire... regardless, just because it sounds cool in English doesn't mean it makes any sense in Japanese. I recommend getting a proper Japanese tatoo if you want that, instead of a translation. Really though, I don't think anyone should get a text tatoo unless they wrote the text themselves and it means something to them. It makes no sense at all to tatoo a translation into your arm if you didn't even make the translation yourself.
It looks like you're new here. If you want to get involved, click one of these buttons!