Bangai-O for the dreamcast, Final Boss.
First of all, the last level is long and difficult. It probably took me 5 tries just to get to the last boss.
Then when you fight him, you probably last 10 seconds at the longest.
If you use a bomb at the wrong time, he counter-bombs you, and you die instanty.
Then when you get him down to about 10% health, he goes invulnerable. You can't hurt him for 15 seconds, and if he gets near you, you instantly die.
If you live long enough, his invulnerability wears off, and you can try to take off his last 10% health. Again, bomb at the wrong time, and you are still instantly dead.
Another tough one: Super Metroid. In the intro, the first time you fight Ridley, keep shooting him until he runs away, without getting hurt down to 30 life or less.