You are not necessarily doing anything wrong. The hardest two AI levels get large to massive economic bonuses, free research, extra capitalship training levels, and other noncombat bonuses. All strategies on beating them requires exploiting AI tactical weaknesses against fortified planets, titans and Caps with AoE attacks, and super weapons.
I personally rarely play above unfair AI, if you can consistently beat unfairs, especially without relying on stabases and those other AI weaknesses mentioned above, you've probably learned all you can from playing the AI. Now you should focus on learning the tricks of the competitive game, either by reading advice on these forums or playing multiplayer yourself.
That said my personal experience with those AIs in Rebellion is that they are very... haphazard. Sometimes they play brilliantly and give you a fight for your life. Other times I can just steam role them 1v1. I'm guessing its the particular AI types that determine this "Aggresive", "researcher etc.", but I'm not exactly sure.