lol @ that graphic.
It's basically like:
"TYPE A: angry assholes. TYPE B: really cool, chill people."
I was like, "This was obviously created by a Type B," and right there on the page is some chick commenting, "lol this chart is so biased the person who made it must be type B."
Anyway, yeah. As the guy who wants to chill, you are not going to dominate a person whose personality is to dominate. I would just put "I need to dominate her!" out of my head entirely.
Instead if I was you I would just focus on having my sphere of chilled out living and try to get something complementary going on with her. Like, imagine "The Dude" from The Big Lebowski dating some fiery chick. She would be going around doing her thing and he would just be in his space, telling her, "If you want to get all worked up, you can, but can you do it somewhere else? I'm trying to enjoy Mother Nature here," or whatever it is he's doing.
It's not dominance so much as it is control of your own frame.
You're chill. It is chill around you. If she wants to come storming in with her fiery demeanor she can, but how about she just cool it a bit? It doesn't always need to be go-go-go 24/7.
That's how I have seen the more relaxed guys (who I presume are Type Bs) with good frames handle their more assertive (presumably Type A) chicks. They don't 'dominate' them... they just maintain this aura of chill and ask that when she is around them she dials it down a few notches and relax a bit.
Chase