How did Batman find out that Tony Zucco killed Robin's parents?

I've been looking all over for information on how Robin's parents died. I've found that a mafia boss/thug (depending on which version of the story you follow) named Anthony "Tony" Zucco sabotaged the trapeze that the Greyson family used. I then found that Batman investigated the crime and discovered the identity of the murderer, and Tony was later sent to the electric chair/life in prison. But _how_ did Batman solve the case?How did Batman find out that Tony Zucco killed Robin's parents?
simple: "HE'S THE GODDAMN BATMAN!" -from All- Star Batman and Robin



and depending on the version, i know that in the animated series (1992) Dick Grayson saw Zucco walk out of the tent with a smirk before his performed with his parents. and so when Batman/ Bruce took Dick in, Dick told Bruce. and then in Comics version, i think Batman examined the trapeze rope and found the residue from this organic chemical used to destroy the rope and he traced it back to Zucco. i think through Zucco's hideout, or a heist he pulled at a chemical lab.How did Batman find out that Tony Zucco killed Robin's parents?
Because he's the Wold's Greatest Detective. Read Dark Victory by Jeph Loeb and Tim Sale. It has a basic telling of Robin's origin.