1) HDMI capture device like the Elgato HDMI Game Capture HD. It's around $170. You'll also need the lightning to HDMI adapter which will set you back another $40 or so. 2) Airplay. Get Reflector and mirror the screen to your computer. It has sharp recording built-in but you can also use Bandicam or Fraps or whatever you have to record at your own desired video quality. Word of warning though: requires a really good network or the video feed will be choppy. Currently on sale for $10.39! http://www.airsquirrels.com/reflector/ 3) Use a camcorder. Unlike the other options, this can capture your gameplay at 60fps. Your hands too
I think I used a program called Mirage, it works really well, you just connect to your computer using Airplay and it records flawlessly. I'm not sure if it does sound though, chances are I might have just not ticked a setting.
You need to enable assistive touch. Settings > Genera > Accessibility > AssistiveTouch > ON You might not get a smooth frame rate with Modern Combat and you're going to see that assistive touch button in your videos. Plus you have to switch to the app to start and stop recording but at least it's a free solution. Just trim the video and you're good.