I played it over and over, but there were parts of it I just couldn't understand. And also, why was it so bad for her to tatoo him, was it bad because he was an outsider, or was it bad because of what she marked him with?

It wasn't that she gave him tattoos. It's that she "marked" him with symbols about who he was. She used HER GIFT on an OUTSIDER. That was her (and Jack's) "crime." In a sense, the misuse of a gift like this was dishonoring to her family and to her people. (Jack could have a good conversation with Mr. Paik about family honor, I suspect! Might help him grasp the concept better. Or not.)

Anyway, if Achara had just given Jack, say, a "5" and some stars, her brother and his thugs would've thought nothing of it. But that's not what she did.

I played it over and over, but there were parts of it I just couldn't understand.

Oh good - I also could not understand over half of what she said. Any help?

I also found it interesting that those thugs KNEW Jack had been marked. Did she tell them? She also mentioned to Jack that there were consequences if an "outsider" was marked. That was the intriguing piece of information I picked up.