I must admit that I have not won any big cosplay competitions (but I haven't entered any large ones either). I do know a number of people who have won big competitions, interviewed cosplayers who are also judges for a University project, and last year I interviewed Euro Cosplay contestants. So although I can't say this is 100% guaranteed way to win competitions, but is more of a guide put together using other people's experience as contestants, judges, and lovers of cosplay.
This is probably obvious but the costume needs to be made by you. No commissions, no items made by other people are allowed. A cosplay competition is to show off your own skills, not someone elses.
When the judges know what the character you're cosplaying is from the more likely it will stick out in their minds. But recognisable doesn't have to mean popular. For example, there are so many Frozen and Attack on Titan cosplays now that it's hard to pick any one from the crowd, and in a competition there is likely to be more than one of those entries. Avoid them because judges are less likely to pick out something they have seen 100 times before. But likewise a costume based on an original character might be impressive but it's less likely to stick out to someone compared to a character they recognise.
Sewing is the basics of cosplay so getting this right is important, but sewing alone won't be that impressive unless it's really something unexpected. A few things that are impressive is a lot of hand sewing. I know a few people who won honorary prizes for sewing 10,000 rinestone crafting bead onto a dress for a Blue Fairy costume (right), which made the costume sparkle on stage from the reflections of the photographer's flashes. Another girl who won a sewing award hand sewed an Amira Halgal from Otoyomegatari by using traditional Eastern European sewing techniques to match the Turkish style of costume. Embroidery like this, or of designs on the costume, is another things that impress judges. You can easily put embroidery in when there is a design or pattern on the costume (rather than painting them on which a lot of people do).
Props and/or Armour Making Skills and/or Electronics
Showing off your skills at making things that aren't made of fabric are a big boost. A lot of people do this through armour and prop making. Various techniques and materials can be used for these so what you create is limited only by your imagination. What's really impressive is if your prop or armour can do more than what it appears, such as having the ability to move on it's own or with puppet techniques. Another thing that people are using is adding lights and sounds to their costumes with electronics.
Having a tidy wig and works well with the costume is also a big plus, especially if it was something that was hard to make.
Accuracy - Fabrics and Make-up
Accurate colours and making the details as exact to your reference pictures as possible is really important. But it's not just accurate colours, but think about how accurate you can make the fabrics. One person won a competition based on the amount of research she did on the kinds of fabric they would have had at the time of the show, making even the fabrics accurate to the period of the show.
Makeup is also a part of accuracy. Having good makeup can really make your costume pop. Even if your character doesn't wear make-up you can use tricks to make yourself look more masculine (if you're cosplaying a boy), skinnier or older (using contouring), and even using a base of foundation will help you look the part and make photographs look better.
Being Judged --> Show Your Off Your Skills, Process & All the Costume
If the contest you're entering in has a one-on-one with the judges it's the perfect chance to show off everything you've done. When you enter a contest you'll be asked to enter a reference picture, but it helps to prepare a portfolio of you reference pictures (not just the character but close-ups of certain details and parts) and detailed pictures of your progress. Hand this over asap as you won't have much time during the judging process.
Go over your entire costume in quick detail highlighting techniques used and show not only the outside but the inside of the costume. Being able to take off parts to give to the judges to look over helps too as they can see your skills and neatness up close.
Really emphasise on the parts that were difficult to make, the techniques you used and what things you learnt on the way, referencing the progress pics where you can. Practice pitching your costume beforehand!
When you perform in front of an audience you may or may not have to do a skit. I think that either way it's good to have some kind of entertaining performance. But a cosplay competition is designed to show off your costume, so having lots of on-stage props is too distracting from your costume, and just walking on and off the stage is too simple.
If you have to do a skit tell a story, you can do this using music or with pre-recorded voices. Try and work a way to show off the costume at the same time. It doesn't even have to be something complicated, such as taking off a jacket because your character's hot. The girl who did the Otoyomegatari cosplay dressed on stage (from her character's underwear) because her costume had so many layers.
If you don't have to do a skit and it's just a walk-on-walk-off it's important to move slowly, pick and plan poses that show off various aspects of your costume, and try and hold your poses for 15-20 seconds, while counting in your head. This is for the benefit of photographers in the audience to adjust their cameras and get some good photos.
Speaking of photographers, if you get a choice of lighting for performances or walk-ons AVOID any coloured lights and lights that change colour or go from dark to light very quickly. You might think it has a cool atmospheric effect but to people trying to take photos is a massive pain and you will have no good photographs afterwards. Keep the lighting simple and bright to show off your costume and performance.
The performance is about entertaining people and showing off your costume.