I just wanted to see what Cake would say.
Now that Cake has posted, I'll give my impression. There's a disproportionate number of Jigglies here in NC, so I've had my fair share of encounters with them.
Jigglypuff has a lot of trouble approaching ZSS. The latter has good range on her aerials, good projectiles and good counters to Jiggs' aerial shield pressure game. Jigglypuff will also find Rollout to be very frustrating against ZSS, as it is easily stopped up by stun attacks, Plasma Whip and bairs. The usual tricks of aerial camping just out of ZSS's range won't work, because that means being at a completely unthreatening distance.
Your best approach against ZSS is probably a FJ or DJ FF autocanceled dair, but even that's risky because it telegraphs itself, and can be countered by a sufficiently defensive ZSS. You might also try Pound for its higher priority. FJ FF nair may also be a good idea, although I've never seen it implemented. Once you're in, keep the pressure, but be prepared for escape Flip Jumps, nairs and uairs. Do everything in your power to get ZSS above you, but even if she's above you stay wary that she can always use a dair, although she'll be leery of it. The main idea is don't get too complacent just because you have a positional advantage.
Jiggs is actually one of the few characters who is decently equiped to properly gimp ZSS. Get below her and be prepare to react. Generally, you'll be using Pound here. If Flip Jumps, try to be in a position to rising Pound her. I believe you should be able to hit her out of her kick, although you shouldn't quote me on that. Definitely be ready to pressure her off the stage, though, in general. Your process should be: Punish her second jump (she'll probably use an UpB boost), then punish her Flip Jump, then edgehog. It will be tough, and a smart ZSS will be able to keep you guessing, but with Jiggs, you have a much better chance than with most other characters.
