When it comes to bringing out your character, was it in story, or art, be comprehensible.
Think through more than twice what your character is doing or saying. Does it fit how you've made them? Does it bring out the message you want? If it doesn't, what could you do different? Should you keep something, or throw it away? Does it make sense in which order you've done everything? Should you change some parts around or decide on different point of view? Rewrite, sketch and change it and do it differently. That will open the possibilities that you might have missed something the first time, or found out something isn't necessary. Just don't delete the old ones. You need them to make the comparison.
Most important, when you share your character design/story/comic, is that not only you understand it, but those who you're sharing it with as well. Is your font clear? Did you do the text by hand? Is the grammar properly executed? Or does your character have a speech pattern that you'd like to e