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From my experience, I can tell that people who rely on B attacks (whatever character they are playing) are not the hardest ones to beat...
Jigglypuff's best move is undeniably his Neutral Air. It has been considerably been given power from Melee/Brawl/PM/SSF2 to Smash 4. It now sends far forward (or backwards, depending from where you hit), has a very long time range and an overlarge hitbox. So I'd say that you should learn to master short hopping and doing Neutral Airs everywhere, you'll manage to edgeguard even a Lucario (true story, I did that once : He always managed to come back since his up B makes him go further and further the more damage he receives, but one last hit and he was out before being able to do his p B).
Something else that you can notice is how fast he is to land. You can come on someone during a Neutral Air, land before your time range is over (so your opponent still shields) and sometimes grab him before he does if he is not reactive enough. You'll never be able to do this with Marth without some kind of cancelling.
When you need to come back on stage do not jump too much, only do this when you are really sure you need to go up, and don't forget about your side B. Not only it makes you move forwards and you can repeat them, but it also has one of those overlarge hitboxes that allow you to extinguish any projectile thrown at you while you are trying to come back, or even an opponent that would like to edgeguard you.
Forget about your up B though. Except if you are fast enough to let go off the ledge, up B, grab the ledge again during the up B but your opponent who was waiting for you is now asleep and waiting for your rest. Otherwise, it is pretty much useless (at least when not in teams) because you pretty much sing while your opponent sleeps so you don't hit anything.
DO NOT SHIELD FOR TOO LONG. If your shield starts going away, stop shielding. You'd better take the hit than lose your shield. If you don't believe me, go in training mode and press shield until your shield wears off, you'll understand pretty fast that it's more of a problem than taking a hit.
Of course, all of that doesn't prevent you from doing some winning random aerial rests (WinRAR) from time to time. But don't rely exclusively on special attacks.