This biome would be rare, and would be extremely dark. I know the bottom of the ocean is already dark, but the trench biome would be 100% pitch black. A flashlight, glowstick or some non-fire light source would have to be used just to see a little bit The monsters in these biomes would all be hostile and deadly. There could also be angler fish based mobs here that let off a slight glow just to give you a bit of a warning that they're coming. Trench biomes would appear as a deep, dark crevice at the bottom of the ocean and would lead farther down and extend for random lengths.
Howabout we make things even more terrifying and claustrophobic and program the AI of deep sea fish to only aggro when you're emitting or near light? The thought of knowing you're surrounded by monsters but being too terrified to look for them is just friggin scary.