From the Reddit thread about this update, it seems that B18 might be a prerequisite for B91 as well, since B91 isn't showing up if you clear B90 but not B18. Folks over there are working to confirm that. If so, you'll be clearing 4-2 with that comp four times, once for B18 and thrice for B91. (Edit: per comments on this Reddit thread, clearing B18 after B90 did bring up B91, so it's confirmed.) Also, for B89, it seemed that you could clear it with a CL flagship and as few as three DDs.
B92... oh, this is fun, not, at least on my third attempt I got to Hoppo and her cute new CG before someone was taiha'd... Hoppo, I got a cute little statue of you for my birthday, please be merciful... The boss node there has to be S ranked three times, btw (info again from that Reddit thread).
@Aredel, edited my original reply a few hours ago to confirm that B18 is also a requirement after Redditors confirmed that. I don't know if I have the ability to edit the original post and if so how to do so, so hopefully mods will catch this. May RNG-sama smile on your attempts to clear the whole chain - B92 is enjoying my salt (just need one more run to make it to the boss node and S rank it, but also need my girls not to get taiha'd on the way...). Edit: complaining didn't quite help, but I managed to clear B92 a minute before the daily quest reset, so also cleared the "heal 5 damaged ship girls" daily right away also. Again, may RNG-sama bless eveyone else still working on this quest chain.