Offensive or Defensive play style?
I'd say a defensive style. I tend to wait and see what my opponent does or bait them into an option. I tend to only push when I think I got a read or when the opponent is in disadvantage.
Grounded. It's kind of hard to play a very aerial based style with Zelda, given her small and relatively laggy aerials.
Moves to prioritize vs moves to avoid
It depends on the situation. The only move I personally feel is too lackluster, is Up-Smash, and it still has its uses. Up-Smash is pretty unsafe and it does relatively lackluster damage compared to any of her other kill moves, with no possibility of follow up. It will probably be decent on stages with a short ceiling, but I tend to find it underwhelming on places like Battlefield. I tend to use it when I need to catch low airdodges and not much else.
Up-Tilt for opponents approaching from the air, Nair for contesting neutral space. F-Tilt, Jab, and D-Tilt are good for close range on the ground. F-Tilt for slightly further away opponents. Jab and D-Tilt for when they are in your face. Phantom for long range and covering approaches from afar.
Those would probably be the ones to prioritize. The rest have their uses, but are going to need more setup or have special uses.
I personally like Up-Tilt strings, usually chaining into Up-air and Nair. Often can get 50% in one go. I also like Phantom into Up-air ledge traps too.
Bad habits you see Zelda players doing that they should work on fixing
Spamming Nayru's Love and Farore's Wind is the most obvious. Lots of online Zelda's have trigger happy Nayrus and while that works on most, players experienced with fighting Zelda, including Zelda mains such as myself, will be able to exploit that. These Zelda players need to learn how to navigate neutral and deal with approaching opponents properly or they will be doomed to be punished by patient players. They also seem to use Farore's Wind when they are having trouble getting a kill or to escape pressure. This may work once or twice, but an opponent is going to wise up and play cautious, and the Zelda player will be right back where they started and giving their opponent free openings.
Another one is playing a very aerial based Zelda and spamming Lighting Kicks everywhere. This may work alright online for the same reasons above, but LKs are too laggy for this to be a viable strategy on good opponents. Good opponents will either move back a bit and punish the endlag or shield and then punish.
A big one that all Zelda players were guilty of at one time and even high level Zelda players still do from time to time (myself included) is use dash attack to approach. Dash attack is laggy and is one of the moves your opponent is going to expect the most. It might seem like you are going to hit, but it usually is your opponent baiting one. Dash attack should be used more as a punish or comboed into or to intercept an opponent's approach. Use Phantom to cover your approach or be patient and move up cautiously, taking care not to commit to anything obvious or risky.
When you do win neutral, keep pushing forward into advantage. Don't win neutral and then fall back to charge Phantom, you're just giving up your hard won space.
Don't be tempted to run up and grab a shielding opponent. Zelda's too slow and her grab is too laggy. On an opponent camping in shield, charge Phantom to it's full extent and then move with it to shield pressure, taking care to watch any jumps out of shield the opponent may do. Alternatively, see if you can feint and bait your opponent out of shield. Grabs should be more about reading an opponent and punishing, not as offensive tactics.
Edge guarding techniques you use most often
Phantom and Din's Fire for opponents recovering high, Dair and Nayru for opponents recovering low. I tend to use Dair for recoveries without a hitbox and those with a hitbox that are linear and easy to hit, that I can at least trade with favorably. For every other low recovery, I tend to use Nayru. Nayru can be tricky to edgeguard with, but if done right, you can even edgeguard the likes of K. Rool.
Pro Controller. Right stick set to tilt, R set to jump, ZR and ZL set to grab, L set to shield. The rest are at their default, I think.
Tips on how to pull through on bad match-ups
Patience and keeping calm. The worst thing you can do as Zelda, is to panic or get flustered. She falls apart harder than probably any other character when her player gets flustered. Keeping a good mental state is something you're going to be doing the entire time you main her, if you want to succeed with her. There is no MU that's unwinnable as Zelda. Even her worst are still winnable as long as you don't let their very flustering style fluster you.
Any other hints, tips, tricks, or techniques you want to share
Never give up. I mean that quite literally. Always make your opponent fight hard for every inch and don't let them get anything for free. If Zelda can take any stock in a few moves, then it doesn't matter how far behind you are. All it takes is a few big plays to turn even the worst case scenario into a clutch. The more you deny your opponent, the more frustrated they become.
Mind games are important for Zelda. The more frustrated your opponent gets, the more likely they are to become overaggressive and leave themselves open. If you can get your opponent fishing for kills or neutral wins, that opens up the opportunity to make big plays. Every person I've known, has gotten frustrated playing my Zelda. Even the few renowned players I've played, all got visibly frustrated, either in their play or on stream. I've come back from two stocks down plenty of times, by getting into my opponent's head and exploiting their frustration and fear.
Relish the fact that people hate playing against Zelda and do what you can to keep them off balance mentally as well as physically in the game. The more stupid kills you can get, the more likely you can start a feedback loop of frustration and anger that will get you more stupid kills. A calm and patient opponent, is a very difficult opponent.