Hey, I'm gonna comment play by play. Feel free to critique/disagree with/discuss my critiques.
I use the term burst range a lot. It's a term in fighting games that means the range where the opponent could hit you faster than you could react (in other words you can't block on reaction, you can only block in time if you guess correctly that he will attack).
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2:08 : Match starts. You dash dance on a platform.
You want to get good stage position asap and/or counter poke at one of Marth's immediate options out of spawn. Since on PS2 you spawn pretty far apart, you should probably just drop down asap and start stealing as much space as possible while not going deep into his burst range.
2:10 : You come down with a dair.
It's true that sometimes you should come down with aerials, even though this isn't safe, simply because you don't have many options. That said, don't lose sight of the main objective. You are not trying to hit him, you are trying to safely return to neutral. Do an aerial that protects you best, like in this case fair, rather than the move that would net you the biggest combo (dair). Save moves like dair for when they made a mistake and are clearly in enough endlag for you to hit with the move for free.
2:14 : You shield Marth's dair and roll away.
Any time Marth hits your shield and lands near you he's screwed. If you see Marth coming down and know he's gonna land with unsafe spacing, then get ready to shield grab, up smash out of shield, or if it will kill him, up b out of shield.
2:15 : Now close to the ledge with few options, you jump.
It might honestly be better to retreat to the ledge or go for a platform sometimes. In this case Marth retreats way too far and it would have been a good opportunity to steal the space back and keep neutral rather than keeping you staggered (staggered meaning at a disadvantage, like being above someone or being cornered by the ledge ect)
2:17 : You shield grab and pummel, then Marth struggles out.
The shield grab was smart. Make sure you only pummel at later percents.
2:18 : After the grab break you roll towards them.
In the uncomfortable situations where both players are clearly in each other's burst range, it's often smartest to dash away. Rolling is vulnerable at the final third of the animation, and can be punished by anyone who knows this and doesn't prematurely commit to an action during/before your roll. As a side note, in situations similar to this like when someone techs away and you can't reach them in time, you can go for passing them -> pivot grab. It sounds weird, but since they have a frame disadvantage, they will likely go for shielding or spot dodging. This covers both options since it delays the grab long enough to grab after when they would spot dodge. Also, if they choose shield, they will likely keep shielding simply because they are waiting to act out of shield after something hit's their shield.
2:19 : After your roll you go for a down smash and get hit by Marth's dair.
Marth didn't punish the roll in time so you were able to act. Since he jumped in once again with poor spacing, you should instantly think to shield -> punish out of shield.
2:20 : After you get hit, you go for another dsmash and get hit by marth's f-tilt.
Once again both players are uncomfortably in each other's burst range. You have a frame advantage so you could have dashed at him which may have scared him into shield/spot dodge (and then go for pivot grab). That said, you're so close that turn around -> jab or f-tilt would be reasonable options. Especially since your frame advantage isn't enough to ensure he'll go for the defensive, making run past -> pivot grab unsafe. As per usual if you are uncomfortable with any of these, dash away and punish whatever he does is also a solid option.
2:21 : You roll away, possibly because you accidentally shielded and wanted to get away(?)
Dash away was your best option. You want to be out of his burst range but you don't want to give him more space than he's earned, and roll away definitely gives him an opportunity to gain back some control. Remember how you reacted when you were by the ledge? You didn't have solid options and ended up jumping even though Marth's shield -> OoS options beat all of your aerials (assuming you don't hit him before he can react, aka hit him shortly after jumping). That said, once you were in shield, you were a safe enough distance away to simply wavedash out of sheild away, which would have would have both prevented him from stealing much space and opened up the option of tilt's and jab.
2:22 : You hit Marth with dash attack.
While it did work out, keep in mind this move is risky. If you predicted the jump, shield is better. This Marth is way too aerial crazy and you should punish him for it. The second he jumps is the second you stop fearing grab, and your OoS options are good.
2:24 : You jump after Marth and Nair after hitting him with up smash.
Since up smash won't lead to true, still in hitstun combos against Marth, and Marth still had his second jump, it is better to stay grounded and cut off his options for a safe landing using your fast dash speed. Remember, if Marth lands near you he's screwed, and when you are on the ground and he's in the air, you are much faster than him. If you shield and he second jumps you can wavedash out of shield to stay under him or jump to chase him now that he doesn't have a jump (but make sure you come at him in a way that you can out range him, which is hard for Marth in particular).
2:25 : You land and shield Marth's falling dair. and roll towards him.
Up smash might not hit, but nair OoS would. Also, if you didn't know, you can smash the joystick left during the hit on shield to move left (you won't roll because you are in shield stun, this is shield smash DI). Smash shield DI can risk accidental rolling, but it can be useful at times. You can also use the c-stick, which takes priority for roll/spotdodge/jump out of shield inputs but moves you less than the joy stick does for shield smash DI. So for example you could smash left with the joystick and right with the c-stick so that you will either slide left in shield stun or roll away. This is called "option selecting."
2:28 : You're on a platform and just shielded Marth's uptilt. You full hop out of shield to escape the pressure and nair.
Your objective is to get back to neutral. The way I see it, once you shielded the up tilt you either had the option to wavedash away and go for a run off fast fall bair to cover your landing, or you could full hop (short hop is risky since his uair outranges all of your quick aerials and he could hit you before your nair goes low). Once you jump, you want to go for a nair if you see him jump, since he can no longer shield. If he doesn't, I like to go for heatwave to either cover my landing and/or boost me safely away to let me land. He did jump but I'm not sure it was early enough for you to react so personally I would have gone with heat wave. Either way, make sure you don't miss that fast fall if you nair and he's far below, as you ended up nairing at nothing
2:30 : You're back on the platform and you shield as he short hops under you.
This is why being on a platform sucks. You can't punish him out of shield and your shield shrinks over time. He chooses to delay his up air, which is smart. You probably should have stayed in shield until he hit your shield or landed. If he just lands, then there's very little landing lag and wavedash out of shield is unsafe since he might instantly uptilt. Also, don't forget to tilt your shield downwards so that you can't get poked. Lastly, while I doubt this player does this, be wary of second jump -> waveland -> grab in situations like this. It's slow enough where you can react to it, but even so your situation has likely gone from bad to worse, especially if the character you're facing has jab/grab mix ups and/or shield pressure options.
2:31 : Marth hits you with uptilt and starts to chase upwards by landing on a platform.
Since he is on a platform, he has limited his ability to chase left and right and he gets on the platform when you're still well out of his reach. As such, either heat wave or second jump -> heatwave to burst you away would likely allow you to either land on the ground or at least the opposite platform.
2:37 : You shield grab Marth and back throw him onto a platform, then immediately jump at him and nair.
Zard can reliably punish all of a character's get up options and/or tech options on reaction when he is under them and grounded. Instead of nairing, you should dash and then crouch to stop right under them (or wavedash if you're still in a dash). Then, react to his get up options (or tech options if you got there in time). If you are there before his tech options: no tech or tech in place means you should up tilt (better follow ups) and tech roll means you should follow -> up smash. If you didn't get there in time to cover his tech options (like this time), then if they missed the tech you can still punish them in a similar way, though it is slightly tighter timing. Use uptilt once again to punish stand up, uptilt but delay it to punish get up attack, and follow -> up smash to punish the roll get ups.
Sooo that was a lot. One thing I'll add is that at 8:08 you might have been able to glair after that sourspot uair. Regardless, make sure you react to DI rather than input a combo before you know it can hit. There might be a few combos where a read is needed, but for the most part you should be able to either follow a combo on reaction and/or cover all their options so reaction isn't an issue.
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Also, most of the time I say you could shield you could also crouch cancel and possibly have better options... Marth's sweetspot dair will eventually break CC and nair will at higher percents, but that's about it. If Nair is autocanceled you won't have much time to punish it, but that requires him to do an early rising nair, so you'll know early in his jump whether or not to worry about that.
Shield is recommended so often by me not because it is the end all be all of the neutral game, but because the player didn't respect shield as an option and so you should have abused this fact. Generally speaking, if your character doesn't have a safe aerial -> jab/grab mix up, nor can they shield pressure, then landing anywhere near a shield means that character is screwed. Since Marth and Zard can do neither, we need to be VERY careful on our spacing when taking to the air in neutral. If you're not going to cross them up, then don't hard approach in the air (again unless you can be safe on shield with shield pressure or aerial to jab grab mix ups like C. Falcon). Instead only jump to "counter poke" what you think they might do.
The characters that can safely land near both shields and a crouch canceling opponent are in the minority... I'd say spacies, maybe Lucas and Lucario because of their strong shield pressure options, and C. Falcon and Mario because of aerial -> jab/grab mix ups. Maybe a couple others for the jab/grab mix up reason, but the aerial has to have low endlag (and it needs to break CC, so said move will probably will be a multihit) and the jabs have to do enough damage to have some semi-decent shield stun and/or have a soon enough interrupt for the grab to be a threat. Also maybe Mewtwo and Peach when they use float/hover cancel, since that leads to one of the few true frame advantages on shields.
Hopefully I don't sound too critical. I make lots of these mistakes as well despite knowing better, so sorry if you already knew all this. I know I break all my rules when I'm nervous :s
Great job on the match! I hope this helps!