Update:
I recently was able to steamroll Berrios and Walter Johnson, scoring the requisite runs with plenty of outs left.
Got to the final boss and forgot to set my lineup.... Arrrrrrggh. I was down 6-15, finished 11-15 with a runner on. I hit 3 perfects that were flyouts to the centerfield warning track which would have made the difference.
I feel like I am definitely close to being able to succeed at this now, as well as beat a bunch of these. Tried the 1st Inning showdown and rolled the 1st Boss there (Rockies Pitcher?).
I find the keys are to know your pitcher/opponent and go for the best hitters versus that side. If its a fastball pitcher, try to wait on a fastball in the upper 75% of the strike zone.