Huh, only one mention of Wiegraf/Velius from Final Fantasy Tactics? I guess only one other person has played that game. Unbelievably hard boss whose 2nd form has 2 ridiculously overpowered henchmen which regenerate, plus 100% success-rate ranged petrify, the most powerful summon in the game, plus the fact that your save becomes "locked" so that most people end up having to restart the game from scratch to beat him? That, plus a first form that can actually be impossible to beat if you are not ready enough? The most common way to beat him is basically to cheat, and then you can only use that method if you happen to unlock the right moves by chance. If that's not a candidate for hardest boss then maybe I don't understand the criteria. I'd vote him hardest just on the premise of "most controllers broken". Even knowing the fight was coming and preparing accordingly, I have still had a tremendous amount of trouble even on like my 4th playthrough.
Second would have been the flagship from FTL until I played enough to figure out how to beat him with some consistency (that is, as long as I don't have really bad luck along the way). If you need tips: There are a handful of strategies that really really help... it's very important that you get a teleporter with any 2 competent crew members (even 2 humans); you can easily knock out the triple missile launcher by teleporting to it right away (it's isolated from the rest of the ship so you only have to deal with 1 crew member, and once he's dead it can't be repaired until the next round). You can also use this to knock out the rest of the guns, which makes it so that the "drone attack" or the 3-rd form super attack are not able to break through a 3 or 4 shield setup. Cloaking is pretty useful also, but not required... you can use it to "dodge" the drone attacks, and even the triple missiles from the first form. 4 shields is useful, but I've scraped by with 3... at least 3 shields is a must though. Having a defense drone or 2 is extremely useful against the second form because they shoot out the boarding drones that the flagship launches (at least most of them), and can shoot out the missiles if you don't have a teleporter to knock out the weapons yourself (also, it's good in the third form so you can shoot out the first few missiles while you are whiddling away at the Zoltan shield). If you find a hull repair drone, that thing is absolutely nuts and highly recommended; it will really cut down the pressure, especially between each of the flagship encounters. The last and possibly most important thing is that you will need enough firepower to knock out the shields... that, or you need a huge stock of strong enough missiles. The best choice for weapons to get along the way, in my opinion, is just a stock of lasers that shoot multiple projectiles per shot. Having 2 guns that shoot 3 projectiles each has consistently proven to be enough for me, and stacking a beam or a missile to that gets the job done. I haven't found the ion beams to be as effective against shields, personally. Also, pause often, especially when you are dealing with boarders on your own ship. Keep at it... I thought the fight was impossible after my 5th consecutive wipe, but once you really figure the game out, it's not so bad.