The Vcore fluctuation can be from a couple of things, and it's not always BIOS related:
1. The system PSU may not be strong enough. Most PSUs don't put out their advertised Wattage, and if they do, it's usually a maximum that can't be sustained very long. You may be right at the edge of what your PSU can deliver right now. If you go into the BIOS and look at the +12V and 5V rails, and they fluctuate a lot, it's usually a good indication that your PSU isn't up to the job.
2. The sensor chip may not be reading the voltage sensor correctly.
3. You have a possible MOSFET problem. This is potentially serious, or possibly not. In the worst case scenario, the MOSFETs are weakened or failing, and no longer are able to supply a stable voltage to the CPU. Over time, the voltage drift will get larger, or the FETs will fail altogether and either cut off the Vcore, or short out and raise it to 3.3V or higher. In that case, it's bye bye CPU.
4. Your capacitors are beginning to fail.
It's not worth panicking about number 3, because there isn't much you can do about it, other than replace the motherboard. Unless you have access to surface mount soldering tools, and some technical know-how, you can't fix it. A half decent motherboard is relatively inexpensive, so having a tech repair it for you may not be cost effective.
First off, check your power supply in the BIOS, and then with some monitoring software. Speedfan does a nice job of voltages. Keep an eye on the drifting. If it starts to get worse, I would suggest a new board.