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Smash Journeyman
One of Falco's most defining and useful moves is his laser, but people powershielding can greatly diminish the effectiveness of lasers. Of course, this doesn't eliminate every advantage of Falco being the one deciding when to fire, and there are certain tactics useable to counter-act powershields.
First and foremost, simply shooting a laser at an extreme height, either very high or very low, not only makes powershielding mechanically harder (and can sometimes mean it's impossible), but allows you to respond with foresight to whatever comes after the shield. If someone were to powershield wavedash forward or nair forward, you could simply dash forward, under your own laser, powershield back, or block or intercept any attempt by the opponent to gain further ground. Of course, all of the top tiers have ways under high lasers, though Falcon's are much higher commitment.
On the flip side, you could shoot a low laser, which means you can act even sooner after it's out, and approach coming over it. Note that the opponent, too can jump over, and if they powershield the laser and continue to hold shield, they will automatically powershield a "normal" attack.
As you must be aware, even if you weren't of that last tidbit, there are two types of powershielding in Melee: "normal" attack powershielding, and projectile powershielding. While it seems to be the most obvious feature of powershielding, it also seems to be fairly overlooked. Both types of powershielding mean you don't take any shield damage. Projectile powershielding prevents shieldstun and knockback, but attack powershielding allows any kind of action out of shield, and amplifies knockback. In later games, the two were consolidated into one (and acting with anything directly out of shield no longer required powershielding), and something I'm about to elaborate on is something I'd like to think is why, as opposed to Sakurai just randomly changing things.
Projectile powershielding reflects. This also means, as a consequence, a projectile (or item) that is for any reason un-reflectable (so would just knock a spacie out of their reflector) is impossible to powershield. While not relevant to tournament play, an obvious example of an unreflectable projectile is Blastoise's hydropump. There are, however, a number of attacks that produce projectile hitboxes, but are not fired as projectiles, and are of course, un-reflectable. If you've ever performed a black hole glitch, you may have noticed you could get a space animal's side-B stuck in the black hole, and continue to move afterward. The reason for this is also because, Phantasm, Illusion, and Sheik vanish all use projectile hitboxes attached to the user's body, or article hitboxes, as some may call them. This is also what allows aerials to clank with them. Normally, ground hitboxes don't interact with aerial hitboxes, and aerial hitboxes don't interact with eachother, but both are capable of interacting with projectile and item hitboxes (excluding secondary properties like transcendent priority: see the laser). Now yes, Phantasm has a bit more startup than Forward smash, and can obviously be reacted to with a quick attack to interrupt it (and the hitbox trails behind Falco), but given the mindset of someone trying to deal with lasers, this is probably one of the last things they suspect (unless using this deliberately became common place).
So what am I suggesting, actually? Well, as an un-reflectable projectile attached to Falco, and not actually a hitbox on Falco, the first thing to note is that the move is in fact, impossible to powershield, which means if you were to ledge-cancel it, your next attack almost certainly will also not be powershielded. The second thing to note, more directly a consequence of it being a "projectile," and not being unreflectable, is that while the person hit with it suffers hitlag, while Falco endures none whatsoever. This means, with an edge-cancel, you could theoretically start legitimate shield pressure off an unreflectable move. Throw in timing mixups by delaying phantasm, or shortens to mix people up and you have... Well, really, at best, an extremely situational mixup. But one that absolutely beats powershielding, no questions asked.
Now for the best bit of advice to deal with powershielding, now that we've gotten what's probably the ultimate jank out of the way, is to simply control the range: that is, horizontal distance between you and the opponent, and not simply the height, immaculately. In the same way the opponent should try to be at specific ranges to deal with laser approaches, you should try to be at specific distances to combat powershielding, or anything the opponent attempts to do out of shield. Not close enough when lasering, to just get hit, but close enough that you could reliably hit a wavedash out of shield anywhere but backwards, off the laser (and not jumping in to get wavedash back grabbed, but maybe do so if it means the laser hits you and stops you), or being so far away that a powershield yields them no laser backed approach (an even shorter distance that Falco's since they can't dash and have to act out of shield). This range could be the one an intentional Phantasm could be appropriate, so master ledge cancelling it and using it at different heights so you have one more tool in your arsenal, however risky it may be (if laser forward smash can be legitimate close range, there's no reason this can't be, the fsmash is even vulnerable to ICG).
Add in dash dances after lasers, as you should even if they don't powershield, and you have easy SDI out on the laser hitting you, if it happens. Yes, it is often recommended for the opponent to just take the laser anyway, though if they don't want to take damage, approach around (over or under), wavedash out of shield, or powershield it. But you can interrupt a close enough wavedash out of shield, or approach of any kind that doesn't come as you're firing the laser, or at the least avoid it. And the laser is weaker after they powershield it, anyway.
First and foremost, simply shooting a laser at an extreme height, either very high or very low, not only makes powershielding mechanically harder (and can sometimes mean it's impossible), but allows you to respond with foresight to whatever comes after the shield. If someone were to powershield wavedash forward or nair forward, you could simply dash forward, under your own laser, powershield back, or block or intercept any attempt by the opponent to gain further ground. Of course, all of the top tiers have ways under high lasers, though Falcon's are much higher commitment.
On the flip side, you could shoot a low laser, which means you can act even sooner after it's out, and approach coming over it. Note that the opponent, too can jump over, and if they powershield the laser and continue to hold shield, they will automatically powershield a "normal" attack.
As you must be aware, even if you weren't of that last tidbit, there are two types of powershielding in Melee: "normal" attack powershielding, and projectile powershielding. While it seems to be the most obvious feature of powershielding, it also seems to be fairly overlooked. Both types of powershielding mean you don't take any shield damage. Projectile powershielding prevents shieldstun and knockback, but attack powershielding allows any kind of action out of shield, and amplifies knockback. In later games, the two were consolidated into one (and acting with anything directly out of shield no longer required powershielding), and something I'm about to elaborate on is something I'd like to think is why, as opposed to Sakurai just randomly changing things.
Projectile powershielding reflects. This also means, as a consequence, a projectile (or item) that is for any reason un-reflectable (so would just knock a spacie out of their reflector) is impossible to powershield. While not relevant to tournament play, an obvious example of an unreflectable projectile is Blastoise's hydropump. There are, however, a number of attacks that produce projectile hitboxes, but are not fired as projectiles, and are of course, un-reflectable. If you've ever performed a black hole glitch, you may have noticed you could get a space animal's side-B stuck in the black hole, and continue to move afterward. The reason for this is also because, Phantasm, Illusion, and Sheik vanish all use projectile hitboxes attached to the user's body, or article hitboxes, as some may call them. This is also what allows aerials to clank with them. Normally, ground hitboxes don't interact with aerial hitboxes, and aerial hitboxes don't interact with eachother, but both are capable of interacting with projectile and item hitboxes (excluding secondary properties like transcendent priority: see the laser). Now yes, Phantasm has a bit more startup than Forward smash, and can obviously be reacted to with a quick attack to interrupt it (and the hitbox trails behind Falco), but given the mindset of someone trying to deal with lasers, this is probably one of the last things they suspect (unless using this deliberately became common place).
So what am I suggesting, actually? Well, as an un-reflectable projectile attached to Falco, and not actually a hitbox on Falco, the first thing to note is that the move is in fact, impossible to powershield, which means if you were to ledge-cancel it, your next attack almost certainly will also not be powershielded. The second thing to note, more directly a consequence of it being a "projectile," and not being unreflectable, is that while the person hit with it suffers hitlag, while Falco endures none whatsoever. This means, with an edge-cancel, you could theoretically start legitimate shield pressure off an unreflectable move. Throw in timing mixups by delaying phantasm, or shortens to mix people up and you have... Well, really, at best, an extremely situational mixup. But one that absolutely beats powershielding, no questions asked.
Now for the best bit of advice to deal with powershielding, now that we've gotten what's probably the ultimate jank out of the way, is to simply control the range: that is, horizontal distance between you and the opponent, and not simply the height, immaculately. In the same way the opponent should try to be at specific ranges to deal with laser approaches, you should try to be at specific distances to combat powershielding, or anything the opponent attempts to do out of shield. Not close enough when lasering, to just get hit, but close enough that you could reliably hit a wavedash out of shield anywhere but backwards, off the laser (and not jumping in to get wavedash back grabbed, but maybe do so if it means the laser hits you and stops you), or being so far away that a powershield yields them no laser backed approach (an even shorter distance that Falco's since they can't dash and have to act out of shield). This range could be the one an intentional Phantasm could be appropriate, so master ledge cancelling it and using it at different heights so you have one more tool in your arsenal, however risky it may be (if laser forward smash can be legitimate close range, there's no reason this can't be, the fsmash is even vulnerable to ICG).
Add in dash dances after lasers, as you should even if they don't powershield, and you have easy SDI out on the laser hitting you, if it happens. Yes, it is often recommended for the opponent to just take the laser anyway, though if they don't want to take damage, approach around (over or under), wavedash out of shield, or powershield it. But you can interrupt a close enough wavedash out of shield, or approach of any kind that doesn't come as you're firing the laser, or at the least avoid it. And the laser is weaker after they powershield it, anyway.