ZSS' biggest weakness is that at high levels of play, she has nothing that's truly safe. You have to predict or guess what your opponent is going to do and punish it. If you even try to do anything preemptively, you'll get hit and beaten. 

That and she has no huge disjoints on her legs like she should.  

The difficulty of the character has nothing to do with ATs. ZSS is difficult to pick up because she plays completely different to conventional Smash Bros. characters. Her ground game is horribly bad, with only 3 moves ever worth using. Her special game is arguably equally bad. Her grab game is nonexistent, so get un-used to shieldgrabbing. Your entire game plan is to get your opponent into the air, where you can win. Easily. To do this you're constantly fishing for a poke, punish or counterhit. ZSS has amazing OOS options, in the way of dtilt (11 frames), utilt (10 frames) and uair (11 frames), but you need a great reaction time in order to abuse this. In a way she plays a lot like a Melty Blood character, where your aerial footsies make or break your game.

Is there any way you could record the hitbubbles in action and post a video? That would be sexy.