@Megaman... it's Mario on the other side, the 8-bit Mario and Luigi were identical apart from the colour.
@topic... there were 2-3 other purple coin stars I found harder than this one, but Luigi's is perhaps the most epic.
I am going to draw out the route I take on that picture.... but my basic principle was to get as far away from the beginning as possible while touching very few platforms, then slowly come back.