What phase of meiosis is characterized by the attachment of chromosomes to the spindle apparatus?

The phase of meiosis characterized by the attachment of chromosomes to the spindle apparatus is indeed during prophase I and II, but more specifically it is most prominent in metaphase I and II.

In meiosis, the attachment of chromosomes to the spindle apparatus occurs when the chromosomes align at the metaphase plate. In prophase, the chromosomes condense and become visible, and the spindle fibers begin to form, but it is in metaphase I and II that these fibers attach to the centromeres of the chromosomes, facilitating their movement toward opposite poles of the cell during the subsequent anaphase.

Therefore, while the spindle apparatus begins to form in prophase, it is the metaphase stage that crucially represents the alignment and attachment of chromosomes, enabling the proper segregation necessary for meiosis to occur.