Hi,
Without knowing how much experience you have making circuits, I think to get an accurate measurement for AC is a pretty complicated project. I've attached a pdf (Watt_VAR_VA) which explains the difference between apparent, real and reactive power, and the reason being is that I guess what drives the handpiece needle is a solenoid, maybe I'm wrong but that must be reactive power - that, for me at least, is not a straightforward circuit to throw together at all, neither with analog parts nor a microcontroller.
If the solenoid is driven by a squarewave, maybe taking the average would give an approximation of the actual power, but still that's a circuit with quite a few parts and a fair amount of prior knowledge. Unless you especially want to make this yourself, I'd buy a plug-in Wattmeter, save a lot of work and more time, not ideal, nor will it measure power from the machine to the handpiece, only from the plug socket to the machine, but I believe it is a sensible solution.
There are two datasheets for low-priced power meters which can measure and display reactive power that are easy to install/wire for one or three phases, minimum input voltage 28V..., if you prefer that type to a plug-in one, maybe there are others which allow a lower minimum input voltage; and
here's a link to about 283 different ones from an online electronic, etc. parts supplier.