Rat: This is what came to mind predominantly because your Samus is very static. Your typical movement pattern is a mixup of walks, and wavedash back, with a wavedash forward tilt thrown in, and once you get your hit confirm, it's then that you begin your punish. This basic pattern is very strong, but it's not really going to work on a Falcon that concentrates on outspacing you, because he's more mobile and can come in at will. I would really focus on more dynamic movement. If you watch Duck vs Juggleguy at the recent Sweet, Duck normally plays this matchup very statically as well. Juggleguy looks like he's learned the tools to beat it. He dash dances outside of Duck's range, and gets in with shield-safe and crouch cancel safe moves. His recovery has also improved, hitting smash DI wall techs on the utilts to beat Duck's utilt spacing, along either varied height, falling speed, and sweet spot distance mixups. I don't think Juggleguy is a better player than Duck(though by no means is he a bad Falcon), but he definitely played this matchup better than Duck did, imo.
Duck's style is an effective way of beating space animals, because with his static, wavedash oriented, feet planted way of playing, he is in a good position to crouch cancel dsmash or use a tilt to outspace a space animal's approach. He can also react out of shield very easily. However, vs Falcon's movement options and aerial options, I think it leaves something to be desired.
So here's what I think Samuses have to do differently in the matchup:
DASH DANCE MORE. At any point in time, if you aren't moving, your options for where you're going to be are much more limited. A static Samus is not going to be as good a Samus for beating Falcon as a mobile Samus is. Dash dancing also unlocks dash attacks, which are sometimes a good anti air against some of Falcon's approach tactics.
Here are some tips on spacing: Falcons, in my experience, tend to space things in bites. I think I started realizing this when S2J gave me a hint about the matchup by mentioning Hugo spacing. "Yeah, Plup just uses Hugo spacing but he utilizes more options." This got me thinking because I was assured that there wasn't really a way for Samus to beat Falcon's spacing. Like everyone else, I tried all of Samus's defensive options, and nothing seemed to work.
It soon dawned on me: Falcons space in segments. It seems very intuitive, if a Falcon is standing still, to space ourselves at sh nair distance, so that if we actually see it, we can wavedash back and punish. Spacing against his dash dance is no different. What I try to do is to visualize the invisible arcs of his dashing sh nair from each end of his dash dance, and move myself with dash dancing or wavedashing such that if he nairs me from one side, I can wavedash back, and if he nairs from the other side, I can wavedash forward underneath it. Basically, I try to move myself such that he does not have a favorably spaced approach on me.
This is really the basis of the Samus Falcon matchup, imo. It's not letting Falcon get that well spaced nair on you.
That's all well and good and it gets me good hits, but of course nobody has perfect spacing, and he's going to get you with that nair. What do?
STOP DSMASHING. Only cc Dsmash if you are 110% sure you are going to hit him. Good Falcons will lcancel into shield, and dsmashing shield means a free knee to the face into combo town.
CC Dtilt is much safer and if you hit, you can combo with uair or fair to build damage, or nair/bair to push him off stage. If he shields, he can't knee you before you buffer shield. If he knees you on shield, he then has a gentleman or grab mixup. I've found that the best solution I have for this mixup is to attempt a wavedash back out of shield. If he tries to grab, he misses and you get a free dsmash. If he gentleman's you, you buffer cc and dsmash. If he tries a different option, your wavedash back should put you into a decent defensive position to deal with other things, like sh aerials, raptor boost, etc.
Shielding is probably next best, but please be careful with Up B out of shield. It is high risk low reward against Falcon, and if you're not sure it's going to hit, please wavedash out, or nair/uair out of shield if you think he's jumping.
Really though, sitting in shield is not something you want to be doing vs Falcon, I would recommend doing it sparingly. The more you actively move and space yourself, the less and less you'll have to shield.
If you want to take one thing away from this post, it would be to please please just at all costs try not to let Falcon get that perfectly spaced nair on you. The illusion of how stifling that nair is is what makes the matchup feel hopeless, imo. The nair can be avoided with active spacing, similar to how I think the Puff matchup should be played: by actively moving and trying to make the opponent's main spacing move(in Puff's case, bair), awkward at different distances, so they don't get the perfect spacing on you.
I think this mostly covers defense. My next post will be on offensive options: stuffing approaches, aggressive baiting, shield pressures, and edgeguarding.
Darrell, I think I'ma use your color and tag this weekend if I get on video. Hope I don't embarass you.