Showdown+Shark = Shark jumps you
I mean, on 7/7 it might be doable, but yowzas.
And it is somewhat harder on the more connected map types, yes, though on honeycomb sometimes you have a working subset that isn't so bad.
Warheads seem indicated. In general the Showdown is your opportunity to pile on
as much cheese as possible, and still feel challenged. Riots, warheads, crazy bonus ship (and bonus combo) tricks, massive defense-in-depth (especially with core turret controllers), shameless abuse of reclamation, etc. Anything goes. No superweapons needed, though those certainly extend the menu of cheese (and intensify what the AI throws at you).
For your first showdown win you may want to try a somewhat less connected map, and probably 7/7, just because it may require playing in ways you're not used to. And for goodness sake don't turn shark on at the same time