I guess I should explain some of the technobabble, then.

MOSFET - Metal Oxide Semiconductor Field Effect Transistor. Think of it as a switch, which is flipped when it receives a voltage to a certain gate (allows electrons to pass through the other gates). Through this, you can control a really high-power circuit with a really low-power one.
Arduino - a microcontroller. You can program it to do stuff - mostly sending signals to different 'pins' which are hooked into different objects like motors and stuff.
DC boost converter - a circuit that turns a lower voltage into a higher one.
Hall Effect Sensor - A tiny little component that outputs a voltage proportional to a magnetic field it receives (called, unsurprisingly, the Hall Effect).
Aluminum - no reaction to electromagnets whatsoever, in fact I think it's slightly repelled by them. Hence the use.
As for the magnetic levitation, Hall-Effect based stuff has been around for a while:
Tutorial and Experiments on Magnetic Levitation - YouTube
Magnetic Levitation (Hall Effect) - YouTube
As for build: My main problem right now is that I need a truly ridiculous heat sink for the MOSFET for the boost converter - the thing heats up enough to boil water in a few seconds. Voltage was measured at 150V, so the current running through the levitating electromagnet is about 0.8 A (off memory). Given that the strength of any electromagnet is determined by H = NI, where I is current and N is number of turns of wire, my magnet should be very strong once I get it up and running - and for the few seconds I was able to test it, it did in fact seem stronger than with lower voltages (the voltage drops quickly if the heat on the MOSFET is not dissipated).
So, a quick review:
-Voltage boost converter circuit is done. Converts 6V, 4.5Ah to 150V.
-Electromagnet 1 (the one that levitates) is done. This is just a whole bunch of magnet wire wrapped around a large iron nail.
-Arduino programming is, for the most part, done. Once I get the magnets up and running, then I have to write something to send a signal to each electromagnet when their respective buttons are pressed. Arduino also controls a servo (for those claws), and sound effects - all that's done. Still need two logic-level N-Channel MOSFETS (signal voltage is low enough that Arduino can handle it) to control the two electromagnets.
-Lights are, for the most part, done. Still need to do that odd 'disc' just in front of the crystals (the claws attach onto it), as well as the barrel itself - but those will be a piece of cake compared to the previous stuff.
-Electromagnet 2 (the launching one) is not done. I still need to run down to Home Depot and pick up 50 feet of 12-gauge wire for about $13 (a bit low on funds at the moment...) The spring and aluminum rod don't exist yet either.
-The actual body of the gun is not even started, except for the few miscellaneous non-metal parts. Thing is, now that I'm making this out of sheet steel, I need to weld it together. So, I asked my high school Welding teacher. He said he'd do it, but not in a hurry - and we're still working out the details. Fortunately, most of this stuff should be easy - that polygonal shape in the back of the gun, for instance.
In short, most of the electronic stuff is built and running already. Most of the body is not.