It should sound like this.
I have tried:
NSURL* url = [[NSBundle mainBundle] URLForResource:@"Justin Bieber - U Smile" withExtension:@"mp3"];
self.player = [[AVAudioPlayer alloc] initWithContentsOfURL:
url error:nil];
self.player.volume = 1.0f;
self.player.enableRate=YES;
[self.player prepareToPlay];
[self.player setNumberOfLoops:0];
self.player.rate=0.16f;
[self.player play];
but it sounds awful.
What you ask isn't a simple task, the reason being that pitch is inherently linked to the speed that audio is played back. For example, a 10 second sine wave at 100 Hz, when slowed by a factor of two, is going to become a 20 second 50 Hz wave (Hz is related to both wave speed and the pitch you hear). To slow this sine wave down by a factor of two without affecting pitch, some algorithm must work out what sound is missing from the 10 seconds of audio that you're inserting, generate this audio and mesh it with what's there. It's not easy, in fact it's really hard.
Good audio editing programs (for example, Logic Pro) can do a reasonably good job, using some complex algorithms. However, anything more than a factor of a few times is going to produce pretty horrible results, the reason being that it's hard to generate audio that didn't exist before, and make it sound good.
(and how I think the above link sounds good):
Firstly, start of with very high quality audio. Steer clear of 128 kpbs mp3s, they're just not gonna cut it. The more sound information there is to go off, the easier it's gonna be for algorithms to create something that sounds good.
Next, research algorithms that are going to work well for a factor of 600 - 900%. Check this out: http://hypermammut.sourceforge.net/paulstretch/ - it's open source so you should be able to learn a lot from it. Plus, the algorithm is especially made for large scale factors. Bingo!
I'd say some sort of effect (or a couple) have been applied to the final result in the youtube video. The website I linked above mentions that "Spectral Smoothing" has been applied to the audio. Also something like reverb may give the result a better or more interesting texture - some things to play around with.
It's not a small task, especially to do well. Should be interesting/fun though - good luck!