For me, 'That One Boss' was the first boss in FFVIII. Not Ifrit, not Biggs&Wedge - Elvoret, and this bastard takes the prize because he (she? it?) forever scarred my younger psyche. Elvoret wasn't even hard, just totally unexpected. I was breezing through the opening sequence of the game, loving the feel and the (then) beautiful CG sequences - then the counter-attack at Dollet, rolling through Galbadian toughs like Anakin through Younglings (alternately, fields of sunflowers), then...Boss Fight! Not even a hard boss fight. Easy win, Squall Scowls, Selphie doing her brainless blonde bimbo routine for whatever reason... "Oh, sorry player, did I say Boss Fight? I meant BOSS FIGHT!"
Bastard pulpified me in 9 turns.
To this day, that one bit of game, that one stupidly easy boss fight, leaves me filled with trepidation.
Though for sheer "F-YOU" by game designers, I nominate the old gem Freespace 2. This one mission, you fly around in a skimpy little interceptor babysitting bombers. And then A SATAN CLASS JUGGERNAUGHT WARPS OUT OF HYPERSPACE. ON TOP OF YOU. WITH HIS FRIENDS.
Now for those of you who were never blessed with playing this classic, a Sathanas class Juggernaught is roughly the size of a small city, made out of hate, evil and alien space metal. Conversely, the human interceptor is little more than a really fast night-gown with lasers.
I won that mission by hiding under the Juggernaught's wings where a) it couldn't shoot me, and b) the stupidly big support fleet it brought along with it couldn't shoot me.
The one time in my gaming experience when being a craven coward was a good thing.