The characters that can potentially pose problems to Link's recovery are ones who have long ranged attacks or super fast aerial movement. Jigglypuff has all of that.
Each character is different though, so let's look at the ones that give Link trouble starting from the hardest.
Jigglypuff- She can float out there for days and just spam her two sex kicks to prevent your great recovery. Fortunately her vertical aerial mobility is poor, so you can slip under her potential edgeguard by fast falling for a short time once she gets on an even plane with you and then using your upB or hookshot. It's simple, but really effective. They can still catch you if they time a move perfectly, but by then you should be stage side and just tech it and do something awesome.
Sheik- She's really simple to avoid once you get used to it. She will either throw needles (not that great) or jump out with a bair. She might even hang on the edge and bair you. Just recover extremely low against her, hookshot a low part of the stage and then upB. You'll eat a hit that you'll be able to tech and then you can either sweetspot upB or try and hit her with it. On stages where you can't recover low you're pretty screwed, just try to airdodge past her edgeguard and hookshot or drop low with a fastfall and upB. Chances are you'll lose a stock, don't get hit really far out against Sheik.
Falcon- He just jumps out and smacks you before you're even in hookshot range. Dropping low won't help because chances are you won't be close enough to drop low and survive. If you air dodge you just get hit by the second uair he throws out. It's hard. I personally try airdodging through and hope that his uair will hit me towards the stage or my hookshot will hit him. Failing that a hookshot feint can work and covering yourself in projectiles as you come in, which you should always do, is very effective at keeping him from jumping after you.
Marth- He jumps or falls off the edge and bairs you. It's what he does. Maybe he fairs instead, but it's the same silly sword swing since scholars say such shots seem successful. Once again projectile cover is your best friend and so is airdodging through him. Coming up low will generally make you eat a spike or on stage move, so just sweetspot your hookshot.
Peach- Her bair is retardedly good and she can hover at the point you like to recover from. Her vertical recovery is pretty bad. Pretend she's Sheik when she edgeguards you but be wary of the turnips, she can drop them and ruin your day. The upB will usually work to reach the edge as it has good priority, just sweetspot it so you don't eat pain.