How to know that Catwoman side mission is done

Actually, since we are talking spoiler, check this video to see what happens:

Basically everything is ruined, Joker becomes an immortal and takes the city. The game ends, with Barbara Gordon crying out loud over a radio line.

But, if you watch it to the end, the game will rewind to the point of the decision, and let you choose again. :)

I think you're talking about the one in the room with the water. That one's actually above the grates, so Catwoman cannot reach it.

You can get it with Batman by climbing up the scaffolding on the right side of the room and using the line launcher. You'll need to aim for the left side and then change direction when you're above the middle of the room.