I always thought of amplitude to be the variation of size in tricks. Take for instance 4a - many of the tricks are very large, giving them lots of “amplitude”. However, very tech heavy 1a which occurs in a very small square in front of the players chest would have very little amplitude. Freestyles with lots of
“big” tricks, or lots of amplitude, are generally much more entertaining to watch, giving them a higher performance value.
As for “professionalism vs. Cleanliness”, they are in two different categories. Professionalism refers to the performance. At the judging seminar at worlds this year, a judge explained professionalism with examples such as showing up on time, dressing appropriately, appropriate music, not getting angry on stage, etc.
Cleanliness, however, refers to the yoyoing itself. It describes how smooth and fluid the tricks are - clunky, awkward, and jumbled tricks would score low when it comes to cleanliness.
“Showmanship” and “Routine” are correlated, but not the same thing. I believe routine refers to how well put together the freestyle is - Does the player quickly transition from one tricks to the next, or do they have to pause every so often to remember what trick was next?
Showmanship, on the other hand, refers to how the player presented the trick. Did they only focus on the yoyo, or did they look up and smile? Were they completely absorbed with the yoyo, or did they interact with the crowd?
I think it’s really important to remember that at a yoyo contest, judges aren’t just judging one’s ability to yoyo. They are judging an entire performance, both the yoyoing AND the showmanship. Being on stage yoyoing is just as much about entertaining people as it is about landing tricks (Well, actually, it’s a 40/60 split)
Here are the official world yoyo contest judging guidelines. A very interesting read that accurately describes how each category is scored.