AC's story wasn't about finding a cure for a poison. That was a motivating factor that pushed Batman forward, just as trying to find Titan before Joker got his hands on it was a push in AA. AC was about solving the mystery about Arkham City, just as AA was about solving the mystery of Joker's plans in Arkham Asylum.
Whereas in AA you were thrown into a small place you suddenly and conveniently couldn't leave in order to try and foil the plans of the Joker, and doing so required you to discover what those plans even were, in AC you were cast into this place that had been alluded to in the previous game, with a basic understanding of what it was, only to realize that something larger was at work, and you needed to find out what. You go from trying to figure out what Strange is up to, to being sidetracked by the Joker, getting mixed up in the ever-changing turf wars of the crime lords, to being sidetracked by Freeze, to discovering the ruins of Gotham beneath Arkham City and seeing that the conflict is being fed by Strange, to confronting Strange and realizing it was Ra's and Joker separately pulling the strings all along, conspiracies conspiring against conspiracies, ending with a final fight against a character you never saw coming. It wasn't an impeccable and flawless work of fiction, but it was really interesting, and WAY more intricate and thought-provoking than its predecessor was.
And... 3 boss fights? If I were ONLY to count the distinct fights: Two Face, Hallucination, Freeze (my favorite, by the way), Deadshot, Penguin, Grundy, Faux Joker, Riddler, Clayface, that's WAY more than 3. And that's not even counting every boss, because I didn't wanna bother looking it up to acquire a more full list. True, plenty of them were from the side missions, so they weren't mandatory fights, but they were still boss fights. Taking down the Riddler in AC was pretty cool, and all of his puzzles in AC were the best in the series. The gigantic puzzle of Batman's hallucination where he had to properly glide from platform to platform and fight a hallucination of Ra's along the way until a final big-ass fight was also really awesome. But, as I mentioned, my favorite of the boss fights was Mr. Freeze, because of how the nature of the battle emphasized needing to adapt to the changing situation, and at the hardest difficulty you had to strategize your attacks in a certain order, otherwise some of Freeze's countermeasures would lock you out of some attacks you hadn't use yet, and you needed to use ALL of your takedowns to beat him, so that was a nice difference from difficulty to difficulty, as well!
God Damn, AC was awesome. I'm shocked when I hear people say AA was better, because I don't know what warped measuring stick they were using to come up with this. It was GOOD, and it was so good that it spawned this entire branch of the Batman canon (dubbed the "Arkhamverse") and a great game series with a growing history to it. But AC improved upon AA's shortcomings in every conceivable way. But AO being the best? NO ONE comes away from playing the first 3 games and feeling like that. You really are the first...
AO didn't improve upon anything (apart from Bane being GOOD, as I previously gushed), most of its map was just a recycle, it took a POSSIBLE Joker origin story that both previous titles made proper homage of The Killing Joke by emphasizing that they were all just stories in the Joker's head and that he was making them all up, and suddenly making it canon in AO (which is a big no-no), and so on. More gadgets, only this time that doesn't make any sense, because it's a prequel and not a sequel, so where did those gadgets go? More unique boss fights, nothing wrong with that, except they were ALL just boss FIGHTS instead of a mix of fights and puzzles. A new way of approaching crime scenes, also a good idea. A much, MUCH better Bane, absolutely great. But those things don't make AO the best in the series by any feasible stretch of the imagination. AO was predictable, and part of this was because it was a prequel (Assault on Arkham has a similar issue, in that you know Joker, Harley, and Deadshot will survive) but part of it was just being predictable. Even before the final fight with Bane, you KNOW exactly how it's going to go down. You know Batman is going to use his very conveniently acquired defibrillator knuckles to send Bane into cardiac arrest, then reverse the process so that no one dies. You cannot NOT see that coming. Meanwhile, the twist at the end of the City comes out of nowhere, and the final cutscene and its consequences are COMPLETELY out of left field, not to mention one of the best game endings ever. ALSO a haunting and delightful cameo postmortem song during the credits, but that's just added flavor.
I'm of the mind that AO sits at the bottom of the pecking order, but I don't have a problem with the times I see people ranking it above AA or AK. But I have NEVER seen anyone place it at the top, and considering all the pieces of the puzzle, it really baffles me that anyone would. AC all the way. AK's biggest shortcomings is being a "next-gen" effort. Too many games this early into the life cycle of a new console focus on bigger and prettier, and they end up sacrificing content to accomplish this. Bloodborne has the same shortcoming. Not as long as it could be because a lot of the game's resources were put into prettifying it. GREAT game, sure, but games tend to be better designed and considerably larger when the consoles they were made for are older and have been out long enough for devs to "figure them out". This has NOTHING to do with the colossal fuck-up of SOMEHOW making the PC version of AK the worst and buggiest, but that's a separate discussion entirely..... XD