Power tools. You can pick up an
electric angle-grinder pretty cheap, along with some
sheepskin or
wool polishing disks (the synthetic ones'll work, but they wear out in a screaming hurry- with a tank that big, you'll end up spending more replacing them than on a real disk or three.) Use very, very little pressure, and vary the angle and direction of movement on your grinder constantly. No. 7 (automotive) clearcoat polishing compound (or even buffing compound, if you've got -really- deep scratches) is actually a pretty good place to start- it's inexpensive, but works very well. Once you get it smoothed out, you can move to a specialized plastic polish.
It's best to use a separate disk for each compound, otherwise you're likely to carry rougher grits over to your finer finishes, and re-scratch it. It would also be worth it, time and money-wise, to pick up a scrap piece of acrylic, intentionally scratch it up, and practice on it before tackling the tank, to get a feel for how the various compounds cut. Probably the most important, and hardest, trick is to
always keep the disk moving, and use less force than you think you need. You'll be tempted to pause over a deep scratch, and use a bit more force, and you'll end up melting a gouge into the tank that'll take 5x as long to smooth out as the scratch would have.
If you were practiced, you could knock out a tank like that in an afternoon, but the learning curve is kinda steep- I'd reserve a couple days, at least- but that's still a helluva lot less time than it'd take to do it by hand.