This is the match up I have the most experience with, so I'll share what I have learned from it. Please feel to put in your input and critiques, as I am not 100% sure about some of these things. These are just observations I have made while playing these match ups.
1. Stay out of the air. V-13 pretty much out prioritizes everything you do in the air as far as I know. If your up close to her and your approaching in the air, she has way more options than you to throw out an anti air. If your from a distance and your approaching from the air, she can throw out an air dagger and easily combo you, then push you away from here. You only want to air dash in when you see her throwing out a ground dagger. If your able to, stay as low as you can to the ground while being above the dagger(In this case, an instant air dash will work well).
2. Your normals are faster, but her normals have longer range. Pretty much, as you all know you want to stay as close as possible to V-13 during this match up. You can't let her have any distance at all because you literally have 0 offensive options. Noel's projectiles simply are not fast enough as hers. I normally approach from the ground by running towards her. You can cancel your run and instantly block if you barrier guard. You should do this if you see her attacking. Your goal here is to get close enough to throw out a normal or get within grab range and do your normal BnBs from there. Once your inside, chase her techs and continue the pressure.
3. Once your inside, she will of course try to attack back. A lot of V-13s love to spam the rapid daggers at close range. Your 1C goes right underneath that. ;o Another cool thing to do is if they spam 2C, just use your 2D and it'll jump right over her. Remember, don't give her room to breath. Throw out normals like your life depends on it. Also remember what character your playing. Noel is awesome at mix ups, so if their blocking, mix things up and work that pressure.
The hardest part of this match up is closing in. But as long as your not stupid with your approaches and your completely random about it, you should be able to approach even the best V-13 player.