This achievement is missable as you need to pick the right answers to get her after you fight her. Yuffie is only available after you go through the Mythryl Mines for the 1st time and are on your way to Junon. The forests near Junon have a very low chance of having Yuffie appear (12.5%). You will have to get a few encouters to find her, but it shouldnt take to long.
Once you beat her do not use the save point after tthe battle! as she will run away if you do so. Now that you beat her just pick the answers listed below for each of her questions and then she will join you.
1. Not interested
3. Wait a second!
4. thats right
5. Lets hurry on