If you've played the DS version of Final Fantasy III, then you may have seen the secret class known as the Onion Knight. In that version of the game, it is the best job, albeit the difficulty to obtain it and level it up. But this is not an FEOK. Fully Equipped Onion Knights only appear in the NES/Famicom version of the game due to how the Onion Knight is presented. You begin the adventure immediately with four nameless Onion Knights. If you were to compare stats of the Onion Knight to other classes, it's the worst and training this job can be very difficult and tedious.
The difference between an FEOK and a regular Onion Knight are their equipment. If you equip the Onion Knight with a specific set, called the Onion equipment, then it will become an FEOK, as the FF community has coined it. This FEOK is godly powerful and will destroy anything in its path without difficulty. In my experience, I've used only one FEOK and I managed to defeat the final boss with just that one character... at level 45... in three rounds! It's certainly impressive but the downside is the method to obtain the set.
In the final dungeon, the Crystal Tower, there are these dragons that randomly appear. Killing them may sometimes reward you with a piece of the Onion equipment. This is really hard to do as the chances of finding the dragons are rare but even rarer are the dragons dropping the items you want. There is another method, however. A glitch was found (no, not the one with the Old Man and using surf along the shore of some island) which, when activated, would upgrade the item in a specific position in your inventory. For example, say I put an iron sword in x spot in my inventory, and then activated the glitch, the sword would upgrade to steel. Same goes for armor and even items, such as potions and gyshal greens. I won't go into specifics since I'll just leave the gamefaqs guide at the bottom, but this process, although seems easy enough, can take many hours to get a full set of Onion equipment. I believe it took me about 8 hours to get one full set, so if I wanted to get all 4 sets, then that would have taken 4 times as long! "Hey! This isn't first-grade math class!"
So if you ever get your hands on this game and decide to go through but don't want any difficulty, or you want to totally obliterate everything, then try this out!
Have a drink!