From a metagame PoV, by Planescape canon, trying to defeat the Lady is nonsense. Before being an actual entity, even before being a plot device (I actually don't like using her as such), she is the symbol of the setting. By Planescape canon, killing the lady is nonsensical because it would pretty much mean that you are no longer playing Planescape.
In-game, by Planescape canon, defeating the Lady is impossible; the "shadow" thing is only a display, the real effect being that she can kill anything within Sigil including a greater deity, when she wants, with no possible way to resist, without even needing to be present. She also has full and selective control on all ways in and out of the city. This is all well-documented. Basically, you can't affect her from outside Sigil, you can't enter Sigil unless she lets you, and once there you can be killed or mazed the moment you try something. You can't even communicate with her to try some trick. As if that wasn't enough, there is evidence that her powers may extend outside the city as well.
Basically, if you want to engineer a campaign where the Lady is killed, ousted, or otherwise defeated, you have to step out of Planescape canon (which is fine, but maybe not what you were looking for).