Here is how to defeat the Dragon in the final chapter of The Witcher 2 on the hard difficulty.
Strategy: (Thanks to Quaft0 for this guide)
In the first phase try to make the dragon breath fire towards the left or the right and dodge when she does. Then strike her 2-3 times and get out.
Second phase, try to stay close to avoid her flying away. Strike fast and dodge out immediately, quen up at all times (preferably upgraded).