In order to defeat Nancy you must play arcade mode through up until battle 7 without losing. It's advised you have a second controller handy to interrupt the fight when you near death because once you lose, you will have to play through arcade again to face Nancy. It's also suggested you go in to the game options and change the difficulty to easy as well as changing the rounds to 1. There is one move in particular that is an instant-kill that you need to watch out for. She'll aim at the ground with her laser and cut a hole in it. If you are in this area, you'll fall through the floor and automatically lose, sidestepping is the best way to avoid this. The rest of her moves are powerful, but nothing is as deadly as this.
There are multiple ways you can do this. They range from relying heavily on "Heavy attacks" after blocking Nancy for the most part. These are great, but they seem rather risky. x Payload x over on TA had a good method that I've always found reliable, and that's to use Devil Jin and do Forward + X which gives you a moderately powerful kick with a sidestep built in. If you keep spamming this she'll be stunned and you'll avoid the laser in the ground with ease.