What kind of world record you are setting? You can do it the old fashion way of record it external like camcorder or webcam, but your video quality is dreadful. Or record it internal like dvd player,capture card or even vhs to get high quality videos.
If you have psp component cables(don't get composite), you can play psp on your tv that have progressive scan. Then record with a device like a video capture card/device, vhs or dvd player. The difference between video capture card is you skip a step transfering the file to your computer. Capture card records the footage in high quality, so the file size is very large. You need a compressor to reduce size. Another note, component cables doesn't upscale to your tv, so the images are little small. You need bit of editing to crop the black borders or be lazy and leave it alone.
The easiest way to play psp on your pc is to download a custom firmware and use a program called "remote joy". This program allows users to play games on their pc. You can google it or youtube for more details. I'm not very tech savy when it comes to these stuff. I usually ask my friend. And guess what, this was one of topic of discussion. After you get that install, you need a screen recorder like Camstudio or hypercam 2.