I will not bare (undress) with you. I may, however, bear with (suffer) you 
If you have the budget, the soldering part is not super hard. You need to make sure that you can control the LEDs in the way that you need, and drive enough current to do that (probably the hardest part).
You also need lumiwire for the outlines.
So, that looks like at least a 32x32 array of LEDs (smaller out towards the edges.) That makes for ~1,000 LEDs that you need to address to draw one picture. That's a lot of separately addressable latches, and a lot of current -- 10 mA each times 1,000 LEDs is 10 amps of power! Also, it looks like each of those LEDs is actually multi-colored, which doubles or triples the number of contacts.
So, the hardest part is going to be switching 3,000 LEDs on/off within a dozen milliseconds for each "frame" update. I would look at something like a large number of shift registers, and driving them perhaps 8 in parallel for higher bandwidth, and then a set of latches all with a single trigger. If you want to approximate levels with "hand-rolled" PWM, you need to do it even faster.
Separately, you need to generate the image. If that's 1000 RGB pixels, even with just 5 levels per R,G, and B (one byte per pixel), that's 60 kilobytes per second of data that needs to go into the Arduino, which is 10x more than you can drive through a single serial port. Thus, you'll need to figure out some other way to get the data into the device to drive the LEDs, or reduce frame rate, or resolution, or compression, or all three. It's not clear that the oomph is actually there in the Arduino chip to quite get there -- you'd certainly need a lot of optimization. (The similar-powered PIC that was used for that head has 35 outputs, and thus can drive 32 bits plus strobe all at once)
This should give you enough to Google for. I suggest you start with something smaller, like perhaps an 8x8 LED array, driven using shift registers and latches. Once you have that working, you can scale it up!