[Xbox/PS] [2010's] 1v1 Fighting Game

There was a fighting game (player vs player & player vs game) I used to play as a kid in the 2010's that was either on the XBOX 360 or the Playstation 2/3. I don't remember much, but it was like Soul Calibur I think? I remember one character who was a woman and she was all red and fire-y (??) and then there was the "evil" blue version of her who was icy (or or was blue fire?). One of the fights/levels was in an ice cave and I think another was on a pirate ship? I can't remember anything else and I've been Googling forever for this. If you can think of ANYTHING, please help. Even questions to jog my memory would be greatly appreciated.