The song? I don't know if it's the same song, but if you press X over the three teddy bears with astronaut helmets, it's supposed to play some song, not sure if it's Nightmare or not. I haven't really dabbled with the achievements much.
As for the premium theme, go to Multiplayer, and go to the in-game Store. Then go over to Free Offer, and you'll see the premium theme there.
I've heard it twice in one run - randomly by beating a wave. Heard it after wave 14 finished and then again at 27. It's a certain condition you're fulfilling that triggers it. Unsure what that is though.
super hotshot bowser posted... I think the general consensus is that it only plays randomly when both sawblades trap you in the starting room or the other half of the map.
That's definitely a plausible explanation. It kept pissing me off being trapped in one part of the map. Turning it into a "nightmare" to get the path back open. Figured it out, but a pain in the ass nonetheless.