How do I make arcs of movement (for enemies - shmup)

I was wondering how could I make waves of enemies following different arcs (or paths) like shooter games (exerion, r-type, and so on).

I don´t want to think about waypoints and sine is not enough, but maybe try a bhaskara formula on a incremental loop (x,y). Have you seen or tried something like that?

Thanks in advance