How to get +60 FPS in Minecraft while recording footage of your gameplay at 30FPS pinned?

I love Minecraft PVP and since I have been playing lots of it recently; I have been getting quite good every day. Because of this, I'd like to show my friends as well as others on the PVP server I play on how good I'm as well as giving useful pointers during gameplay. Problem is, I must play Minecraft at 60+ FPS or else my skills really start to diminish since 30 FPS feels like 10 FPS in Minecraft gameplay. Is there a way (with Fraps for example) to record at 30 while getting 60 in-game?

No that's impossible.
Recording software and computer fps do not act as different fps measures. Whatever fps your playing at is the fps being recorded. So if FRAPS drops you down to 30fps when recording, then you record at 30fps.
If you were planing to upload it to YouTube, anything above 30fps isn't very noticeable for viewers.

External DVRs can record video without causing any frame loss, since your computer isn't spending any processing on recording.

If by chance you have a recent Nvidia card, it may have "Shadowplay" recording capability that uses the card's built-in H.264 hardware to record with very little frame loss.

Recording software will typically reduce your framerate (as Seloje mentions), unless you happen to have a second system for separate recording.

Don't really know what Seloje is talking about… Unfortunately the way Fraps is coded that it works like a multiplier checkpoint, here are few examples:

1. If you set Fraps to record at 30 fps then it will record at it but will play at either 30 fps, 60 fps, 90 fps or 120 fps. Which ever highest it can keep up with.
2. If you set Fraps to record at 20 fps then it will record at it but will play at either 20 fps, 40 fps, 60 fps, 80 fps, etc. Which ever highest it can keep up with.
3. If you set Fraps to record at 60 fps then it will record at it but will play at either 60 fps or 120 fps. Which ever highest it can keep up with.

So if you are recording at 30 fps and your fps drops even to 58 fps then it will automatically gets locked to previous checkpoint which is 30 fps. This is the reason why some people prefer to record at 50 fps, at least they will get reasonable playable framerate then. Note that YouTube maximum framerate is 30.

If you want steady 60 fps while recording at 30 fps then you will have to improve your computer hardware(specially Hard Drive) or lower in-game graphics settings and resolution and also turn off bunch of background processes that affect Fraps performance(below more about it).

Definitely check this thread on Fraps Forum, it explains how to get the Best Fraps Performance by playing at 60 fps in-game while recording at 30 fps - http://frapsforum.com/threads/best-fraps-performance-tips-afaik.559

Feel free to ask any other Fraps related questions on that Forum too as well.