I wish Billie gave explanations to more of his lyrics, it's always really interesting to hear them.
I always thought of "tattoos of memories" as referring to nice memories you want to hold on to and "dead skin on trial" as referring to the moments you scrutinize your decisions/things you did in the past, beat yourself up for past mistakes ("dead skin") and put yourself metaphorically "on trial". And then it's followed by "for what it's worth, it was worth all the while", which is a kind of reassurance, stating that it's not worth it to beat yourself up over the past.