This guide does have a lot of details. Ultimately how you handle each board depends on your RNG and (if need be) items and space events.

No, the Frightmare does not have an explanation screen.

@Unsupervised, The Koopa Kids actually don't get more coins with higher Story Mode difficulty. It just means the K. Kids will be tougher to beat. EVeryone starts with 20 coins on every board regardless of difficulty.

I'm aware that the only Story Mode difficulty in the leaderboards is easy. Is it possible to include NORMAL, HARD, and INTENSE difficulty categories? (Though i'd probably only attempt Normal).

There really isn't much to explain. Everything relies on the RNG.