Final answer:
During Prophase, the initial mitotic phase, the nuclear envelope breaks down into vesicles, allowing mitotic events to proceed. The correct answer is option C.
Step-by-step explanation:
The phase of the cell cycle during which the nuclear envelope starts to break down is Prophase.
This marks the beginning of mitosis, where not only does the nuclear envelope break into small vesicles but the membranous organelles like the Golgi apparatus and endoplasmic reticulum also fragment and disperse towards the cell's periphery. The breakdown of the nuclear envelope allows the spindle fibers to access the chromosomes, facilitating their movement and segregation during cell division.
The nucleolus disappears, the spindle apparatus begins to form, and the sister chromatids start to coil more tightly and become visible under a microscope.