A bully is someone that attacks you repeatedly all the time, every day. Or if they are hitting you all the time through the day. Remember that when you go on the fight list by Zigna people will attack you until you are dead. This person is not considered a bully. A bully is someone who comes back after you have regain you health. He or she may hit list you several times. This is a bully. Not the person you attack so they hit list you and not the one that attacked you 15 times till your health is gone, 1 time. Remember everyone has the right to defend themselves.
Another kind of bully is someone that is significantly at a higher level that you (ie. 40 - 70x higher), and he/she attacks you, but only goes after you once. This person does not fit the classic definition of a bully described above, but because they are more powerful than you, I put them in this category, not because they were being mean but because they should have known better than to pick a fight with a little guy. It's just good game etiquette not to do that. The exception to this is when you reach level 300 and you are thrown in the deep end of the pool and you gotta now swim with the big boys.
Also be watchful for hits that were strictly hits from fightlist. Watch for multiple hits and the timeframes within. Many people when fighting do not even look at names. We have seen some get hit and iced more than once within minutes by the same person. This again is not a bully.