Month of prep for both.
Too much rides on whether or not Two-Face's coin flips to his favor or not. He's smart and arguably second to the Joker among the rogues, but I don't recall any feat that puts him on par with Ivy. The most I recall him doing is threatening to unleash a deadly binary chemical compound on Gotham. I don't think he can do too much against Ivy's spores, attack plants, toxins, pheromones, and hosts of other nasty surprises.
You can assume that the coin flip is in his favour (due to bloodlust). It depends on which version of Poison Ivy it is (Plant versus Human). At the start, Ivy starts raising up plants and Two-Face will draw his weapon. Tommy Gun, HandGun, etc. If Two-Face gets his shot off and hits Ivy, it's probably over as he runs over, uncaps the industrial chemicals in the jar that he brought with him and burns Ivy alive. If Ivy blocks the shot(s), and/or gets out of visual range, she wins. Her other attacks will eventually gets through.
It comes down to Ivy's dodging/power to block a bullet (as I think Two-face is a decent-to-above average shot). Any aim-dodging feats and/or plant raising to stop bullets?