A Nuclear Hard Death is a Behavior setting in monsters. It is essentially an explosion. However, it is audible and visible over the entire level. When a monster with a Nuclear Death is killed, the screen will suddenly turn completely bright for a second and then steadily go back to normal.
The only monster ever fought in the main trilogy to have a Nuclear Hard Death is the Juggernaut. Though any monster can be altered in the Physics files to have a Nuclear Death. In fan-made scenarios, the Mother Of All Hunters is frequently altered to have a Nuclear Death.
In mapping, there's a special trick which uses monsters with a Nuclear Hard Death. They are situated on platforms not connected to the rest of the level and will be crushed to death by the platform because of an external trigger. Because of this trick, you can make it look like an explosion just happened after doing something, like pressing a button. This is used in the Marathon Infinity level Hang Brain, where the Nuclear monsters respawn in their crushers after being killed, which results in a lot of explosions at unpredictable times, often suprising the player.