#1, you need to start with a clean CAD file. Garbage in, garbage out. If you're working from an auto trace of an image file, you're not going to get good results.The lines in the logo at the top seem a little shakey, but that may be due to the tracing having some chatter in it.
If you have good, clean g-code, then it comes down to machine rigidity. Build your CNC machines are not very rigid. with the machine off, and no tool in the spindle, grab the collet, and push and pull on it. If it moves at all, then you'll have issues getting clean cuts in acrylic. What you might want to do is take a very shallow, final finish pass, which can clean up any roughness.