Batman: Mask of the Phantasm : One question in regards to the movie (Spoilers)

First off, I love this movie. I have watched it countless times and make it a point to always watch it around the anniversary of its theatrical release (in addition to many other times.) There is one blank that I feel I have needed filled in for a while.

How did Joker find out that the Phantasm was Andrea? When he spoke with Reeves, he did talk about being her father possibly (already having killed him himself of course.) Obviously, there was a connection there between the mob bosses that worked together, but how did he deduce that *she* of all people was the one killing everyone enough to even call her and attempt to blow her up when Batman was investigating her apartment?

This detail bothered me for whatever reason. Obviously Joker is a very smart guy and it is reasonable to believe that he figured it out on his own and not everything needs to be outright shown in a movie, but this one struck me a little off.

It could have been anyone, but the Joker assumed it was Andrea because of what he did to her father. I also think that the phone call as Joker pointed out also made it kind of suspicious. Why would she call Reeves out of all times while he and Joker are in the middle of a conversation of the very subject. If you think about, who else would have been committing the murders of the gang?

I have no idea why but I completely blanked on the fact that Andrea made a phone call during that scene and that was the clear correlation especially considering the discussion during the scene.

Just by the time he called and left the message "and there's no way you'll go out the window this time, toots" it just didn't feel entirely like a big wowing moment of that makes sense like I felt it should have been if that makes sense.

Still waiting on the day that this film gets a blu ray release as well.

Same here, along with the animated series.

She's the only one alive that has any reasonable connection to it at all besides Arthur.

Joker
A). Knows it's not any of the mob bosses because they're all dead
B). Knows it's not Batman because of what happened at the house
C). Knows it's not Andrea's Dad as he's dead
D). Confronts Arthur but he doesn't really fit the profile
E). Is there when Arthur receives the phone call from Andrea

All of the murders start happening right as the daughter of someone you've murdered comes back into town? Only logical person left.