The moment Fat Mandetonates in Nagasaki is scary in and of itself, but if you listen closely as the fireball engulfs the city, you can actually hear the screams of the civilians in the city as they are all incinerated in the blast. Most Japanese soldiers there know what's happening due to Hiroshima three days earlier...
The immediate effects on Logan after surviving the Nagasaki atomic blast, and then seeing him very painfully heal from it.
You will wince in horror multiple times in the Self-Surgery scene.
The moment Viper sheds her skin is rather creepy.
The Silver Samurai drilling into Logan's broken claws' marrow and sapping out his Healing Factor. The fluctuation of the healing ability on both of them during the procedure and the fact that it's one of the closest moments Logan has ever been to dying are quite nightmarish.
The actual nightmares Logan suffers with Jean Grey.
The ninjas ground into meat and blood by Yukio. The sounds and the blood spraying onto houses lining the street...ugh!
