It's difficult to tell from the photo how deep the scratches are, but they don't look too bad, so I would start with the Novus 3, 2, and 1 solutions (in that order). If that's not enough, then you would need to start with some really fine sand papers (1000 grit or finer) or lapping paper, then on to the Novus.

Edit: You might want to check in on the thread "Acrylic Pinball: Clearly I'm insane". I do a lot of work with acrylic, but not near as much polishing as he's done.

I would avoid anything that could heat up the acrylic. When acrylic is heated, it develops internal stresses that can be released in the form of small cracks. I tried using one of those oscillating tools with a soft cloth and novus in place of the sanding pad. The piece cracked as I was polishing it. I recommend doing it by hand. It really shouldn't take that long.