The DJI Phantom Quadcopter for the GoPro Hero cameras are still gaining popularity, but getting smooth footage is impossible without a few modifications. The first step is to ensure your rotors are balanced properly, and then start looking into a way to create an isolation mount for your camera. There's been several ideas on how to create this, but this DIY Wire Isolation Mount seems to be a great and more secure solution.
The single wire isolation mount design is adjustable to have more or less tension. A few web searches show how to DIY one yourself, or if you're not the DIY type, check out one ready made GoPro Hero Wire Isolation Mount for the DJI Phantom now available via eBay (click here).
DJI Phantom Single Wire Isolation Mount GoPro