Doug Moench and Gene Colan begin a 4part Two-Face story in Detective 563 (June 1986) that weaves back and forth between this book and Batman.
Jason Todd brings Rena back to Wayne Manor, and in his quest to impress her, he almost reveals his Robin outfit. Or at least, that’s what Alfred thinks he is going to do, just before he stops Jason. Was he going to? Jason says no, but teen hormones do overpower judgement.
Batman and Catwoman are still trying to round up the last members of Black Mask’s False Face Society. Batman breaks into the Sionis family tomb, which he was using as a base. But all they discover is that someone else is trailing them.
As for Two-Face, the length of the four part story means that this issue serves to re-introduce him, and he reflects on his origin. Circe is also re-introduced, the former girlfriend of Black Mask, horribly mutilated by him.
Green Arrow and Black Canary continue their struggle against Steelclaw and Champion in this story by Cavalieri and Moore.
Green Arrow has noticed that all the things Champion has saved had been insured by the same company. He figures that Champion is actually causing the disasters he saves things from, and sets him up. Entertainingly, Green Arrow uses an art exhibit by Ozone as bait, which Champion shows up to set fire to.
Black Canary doesn’t have a lot to do in this one, but does make the vital connection, through the use of the nickname “Brucie,” realizing that Steelclaw is really the mayor.