Former judge here, and only former because I chose to leave due to school and work.
But in my experience. Always bring references, judges are like everyone else, and not everyone knows all the characters in the world. So reference artwork, screenshots, or even a figurine sometimes can help.
Furthermore, You'll want to bring progress shots as well. A picture is worth a thousand words, and progress shots speak for themselves on the level of your work. It's hard to explain to a judge what you've done to make the costume, and its easier to Show AND Tell rather than just tell. It also helps us to determine if the costume is genuine, as in terms of not just another manufactured costume.
When you explain, just work from top to bottom on your costume, or bottom to top. Whichever you prefer. If you miss an aspect for whatever reason, and deem it highly important you can always add it in the end.
Now for the judges.
I've never allowed aggressive judges on my panel. This is a hobby, not a war of costumes. It's like what the other fine cosplayers have said before. If they're rude or aggressive, speak up... say something to the director and the matter will be dealt with accordingly. Usually a person that is rude has a history of being rude.
When I judged, we always told the cosplayer that we were going to look at the costume up front (flipping seams, ect.) . It's a given. Why did I do this? I want to see the work for myself, the creativity, even though I have reference pictures it's still worthwhile to look over the costume while you explain things. It's like... when you build a house, or change your front door you need a building inspector to come by and judge to see if all the fine details are there and the time was really put into the costume to make it what it is.
I personally feel that judges who sit behind a table without exploring any of the costumes that come through do not really know or perhaps even care to judge.
Wear the costume too! We want to see how well it looks on you! How well you've made it to fit you! Hahahaha, I can't think of anything else really. Don't be nervous, have fun with it and above all relish in the victory that you were able to get up on stage and show almost the whole convention your costume! People may even stop you after the show to try and nab a picture.