Since I recently acquired 21 watches in various states of function and condition, I thought I'd share my technique for restoring acrylic crystals. As a warning, there are items used in this procedure which can be harmful if used improperly, so please always read the manufacturer's warnings and heed them, thank you, and enjoy.
I prefer to begin with a dual sided Emory board similar to what is used in nail salons. They're flexible and conform to the curve of the crystal. The one I use comes with 2 different grits, one coarse and one fine, 400 and 600 grit respectively. I dip the Emory board in water and ensure a small puddle forms on the crystal. I begin with the coarse grit and start with a circular motion, applying steady pressure. As I sand, I rotate the watch in small increments being careful to not stay in one place too long and to maintain a circular sanding motion. I follow the natural curve of the crystal as well, unless it's a flat crystal. After a few minutes, I stop and check my progress. I wipe off the water and acrylic residue and look for any obvious, deep scratches that remain. If not, I proceed to the next step, if so, I repeat the previous steps. When I'm satisfied that the deepest scratches are gone, I thoroughly clean the crystal and wipe it dry. I now flip the Emory board to the fine side and repeat the previous procedure of circular motions. Knowing when you have done it enough is honestly an issue of feel. When you first change grits, the surface feels rough and there is resistance as you sand, but that lessens as the deeper sanding marks are made shallow by the finer grit. This process should take less time than the first step. Again I clean off the residue and thoroughly dry the crystal. If im happy the the smoothness of the crystal, I can now move on to the final polish. I use a polishing compound from my employer that works amazingly, however any glass polishing/scratch remover that contains Cerium oxide will work fine. For this step I take a cotton cloth and fold it over twice giving me 4 layers of fabric. I then dab a penny size drop of the Cerium Oxide cream onto it and then press the crystal firmly onto the cloth. I then swirl the crystal around and around in a steady, circular motion, maintaining a firm pressure as I work. I rotate the crystal every few moments and I rock and tilt the crystal following the contour of the crystal. After a couple minutes of this action, I stop and wipe away the residual cream and inspect my progress. Most times, one cycle of the Cerium oxide cream is adequate, however, if you miss a spot, repeat the process. The initial penny size drop of the cream is almost always enough. If you're happy with the results you can wipe away all the residue and enjoy your work.
BTW, cerium oxide will lightly polish metals as well, similar to Brasso. This can help to remove scuffs, light scratches, Oxidation and other residues on older watches. Lastly, this entire procedure can be perform without ever removing the crystal from the case, as long as you are mindful of the case. Thank you for your time in reading this, hopefully I've enlightened you and added a new tool to your watchmaking toolbox. (The crystal used in the photos of this procedure has microscopic crazing cracks from age and heat which are deeper into the crystal and this procedure does not remove those, however, for me it looks great.)