I'll make is simple. No matter how you describe this situation, no one that has any extensive work is going to say it's OK to confront your artist. An estimate is and estimate, it's not a guaranteed contract. She misjudged the amount of work. What would you like her to say???? What could she say that would make this alright?
Better to be mad about the cost than mad because you got a shit tattoo. I wouldn't want someone rushing through my tattoo because I was complaining about the cost.