Catherine’s nightmare part drops Vincent in a tower. The goal is to escape by climbing to the top before the floor shatters and Vincent plummets to his death.
A grotesque monster chasing him is one threat; traps are the other. See the tiles with holes in them? Those are for trap type blocks that turn Vincent into an mess of blood and bones if he steps on them.
Some blocks can be useful like bomb type squares that explode when Vincent steps on them. Bombs also destroy other blocks, which can open a new path for Vincent to explore.
Atlus also gave us a glimpse at three stages in Catherine. This may be considered a spoiler so keep that in mind before you scroll below.