This match up is one of my personal favourites to play as either character. This match is down to who can grab the lead early on and KEEP it. Zelda has a bunch of tools in her arsenal that are perfect for dealing with characters who like to weave in and out. Zelda's fsmash, while quite easy to SDI is a very good option to keep Jiggs from getting in. It has really nice priority, comes out fast and if all of it's sparks connect it will do a fair amount of damage. Zelda covers all angles really well and she will normally space herself away from an edge in the case that she gets gimped or is put into a bad position. Obviously from what I've said, we can establish that Zelda has a beautiful ground game. It's all around quite well built, having a really nice dash attack, fastest down smash in the game, quick smashes in general and a superb tilt game, having a kill set up in down tilt to up tilt.
So how do we get past this wall you ask? Simple. Zelda can't approach. She has this ground game that is superb but an approach that isn't even speakable. She has three approach options which are hardly even worth mentioning. Dash attack, nair and airdodging towards the opponent (lol). Luckily for us, Zelda cannot camp to save her life. If she throws out a dins, get in on her. Nair beats out dins so just weave in and out with nairs and fairs to get in some damage on her. Once you've weaved in and managed to get her into the air. She's done. Her air game is AWFUL. Fair and Bair have tiny sweetspots which you should be able to dodge with ease, when they are sour spotted you can probably punish them. Dair like fair and bair has a small sweet spot, that being said however, it can be LETHAL if you're off stage when it lands. Being the third strongest spike in terms of knockback growth, it's best you be careful when going for the gimp on Zelda, try to stay to her sides because she also has uair in her arsenal. This move, whilst not incredibly stellar in it's hitbox, is a MONSTROUS kill move. If you get hit by this move at about 70 from an average altitude, you are not living. Go and see this for yourselfs.
Pound in this matchup works well when she throws out smashes, because the trade will be in your favor everytime AND she will always become airborne, this is where we have to get her. Obviously once she's in the air, juggle her around, making sure you weave away from her aerials when she throws them out. Most of the time, Zelda will fast fall to make it back to the ground as fast as possible. Airdodging when she can. Bait her airdodges and punish them with fairs/pounds/nairs/bairs etc.
Now onto Zelda's OoS options. She has nair OoS which will catch and punish your attempts to attack her shield. She obviously has usmash OoS which is lethal if not SDIed but overall her OoS game is not very stellar, so just space yourself well on her shield, grab her when you get the opportunity and you're in for some free %.
If Zelda has gotten the lead on you for whatever reason, you have something to fear. Zelda no longer has to approach, she can smash, tilt and punish you. She literally becomes a somewhat "OK" character, loosing the biggest cripple to her character. You will have to be patient here. Zelda is not very good at timing you out so don't worry about that for now, instead start spacing your aerials. Weave in and out when she throws out tilts and smashes, wait for an opportunity and punish accordingly.
If you got the percentage lead first, you have a few options here. The obvious one being to run the clock, seeing as Zelda can't do much to stop this. Or you have option two, get Zelda offstage. If you feel a bit worried that Zelda will get the lead back, you have to apply the pressure here. A good Zelda will be watching the clock against a Jiggs, making she sure can grab the lead. Get Zelda offstage asap. You can gimp her, punish her or do whatever you want to her offstage. Once Zelda is offstage, there is NO reason she should get back. When Zelda uses Fayore's Wind (Up B), when she goes green, you can still hit her, and this will cancel her teleport.
Zelda's arsenal of kill moves look like this: Fair, Bair, Uair, Dair (Offstage), Usmash, Fsmash, Dsmash, Ftilt, Utilt. Yeah. That's alot of kill moves. Dsmash is mainly used for gtfo options, the same applies to the other smashes as well, so it's really just her tilts, set ups and aerials that are going to get you killed. You should be able to avoid these quite easily but should you get hit by one of them, living past 90 is hopeful.
Stages
Now for the stages. You want to start by banning Battlefield. It should be known to everyone by now that platforms help people to approach, this is no different for Zelda. She can punish people on those platforms, set up kills better on the platforms and just generally control this stage FAR better then Jiggs can. Zelda also does well on Battlefield and Castle Siege, but Battlefield is your top priority for banning.
Now for Jiggs. She can take Zelda to FD, RC and Pictochat as her main counterpicks. RC is a bit debatable though. Whilst Jiggs does amazingly there, the boundaries on some parts really make it easy for Zelda to get REALLY early kills on you, I'm talking 50~.
Final Word
This matchup is, as I said before, a battle of who can grab and maintain the lead. Zelda's ground game stunts your approaches whilst your air game stunts her approach(es). Zelda will be killing you far earlier then you kill her, but you should be getting a lead on her much quicker and much easier.