>Would you have one huge set of pecs that can contract all four arms (and if so, how would they move - would each arm be independent or would both arms on each side move together?
Whelp from the looks of that pokemon the arms on his back are powered by a combination of his back and sides, while his front arms his front and sides. He'd be very top heavy though. For movement, them moving together on one side is pointless and a detriment they would of course move independently as for how in terms of brain and nervous system I'd say they would have pseudo octopod like system for their arms where part of the brain relies on smaller parts distributed amongst the four arms to compensate for the awkwardness but wouldn't be truly independent like a squid tentacle.
>or would you have two sets of tits? Would this give you four nipples as well?
No, tits and nipples is dependent more on mating and breeding then arm distribution.
>What about shoulder movement - would it be split, so the top arms can move upwards and the bottom arms can move downwards, or would both sets have full range of motion? How would the skeletal system of this look?
None of the above, they wouldn't really have them anchored to the same shoulder that is way to complicated. The range of motion for both would be almost full range for the back and more limited for the front because full range motion would simply result in the arms getting in each others way.
>How would the skeletal system of this look?
The biggest changes would be the head, shoulders, and back since it looks like his head is partially fused into his body.
>And how much more energy would you need to have an extra full-strength set of arms?
It depends entirely on the musculature of the whole thing, just because he has four arms doesn't mean he has the same sort of muscle distribution typically he'd have less muscles per arm. In fact his arms might be connected similar to a chimp's muscles unlike a human's muscles which would give him more power then a human's arms despite having less muscles for each arm.
Oh, and since he has a central nervous system (unless pokemon confirms otherwise) he'd be much smarter then you'd think.