First, let me commend you, brother, for seeking godly advice (even if it sounds contradictory at times). This can be a real frustration, when you love someone who doesn't follow Christ.
Let me second what someone else has said. It is not YOU who can convince her. Only the SPirit can give her faith and do that work. But it IS your job to share the hope that is within you.
From reading your posts, it certainly doesn't seem to me that your hope is based on Moses parting the sea, or Noah and the animals... *grins* Your hope is in Christ, who defeated death and sin by dying in obedience and sacrifice. For us. Because he loved us. The rest of it, most of the discussions about details and doctrines, and floods and creation/evolution... all of it pales in the shadow of the cross.
I have a LOT of Neo-pagan and Wiccan friends. And they bring up the same arguments. They try to tear down this story or that, or the BIble as a whole. OVer time, I've learned to share what I know about such subjects (and God has lead me to learn a LOT more about them than I used to know!), but even so, I keep trying to bring back the focus to the foot of the cross.
We are sinners. We are wounded, and we hurt others, and we are selfish... even when we try really hard. There is a huge gap between sinful humans and our Holy God. We cannot reach across it. We cannot bridge that gap. Our sinfulness, our human nature weighs us down and we cannot cross. So God became man and God in one being, Jesus Christ. He lived, and talked, and prayed and taught. He suffered and died. Adn then, O then, He rose from the dead. That is our hope. That is the grace that pours down on us from God. His death and resurrection destroyed the power of sin and death over us. His death and resurrection wash us clean, and bridge that gap between man and God. He brings us spotless to the throne of God and presents us as holy and blameless. And the HOly Spirit comforts and teaches and guides and convicts us day to day in our battles and temptations in this life, in preparation for the next.
THAT is our hope. And that is what no other religion has. Every other religion in the world is "works-based." You live a certain way, or do certain things, or follow the seven-fold path or the pillars of islam or whatever. You rely upon your own works to follow divinity.
Christians rely upon Christ. His sacrifice is sufficient. (Of course, the Spirit guides us to do good works, but they are a result of obedience and joy, not a duty we do to EARN heaven. We cannot earn heaven. It can only be given.)
Sorry to be so wordy. I just wanted to bring the focus back to the cross.
If you are interested in learning more specifically about how to discuss the other arguments non-Christians bring up -- the truthfulness of Scripture, etc. -- I suggest you check out the
Apologetics forum. Apologetics is "the defense of the faith" (not apologizing for it). I've learned a GREAT deal over the years from studying apologetics.