So, unlike Falco's matchups versus fast and medium fallers, you stand only to lose by being anything but frustratingly patient in floaty matchups. The Puff matchup basically boils down to locking her in one place on the ground and keeping her there until she messes up and you can start attacking her.
Let's start with Puff. Remember that Puff has the best aerial movement and control in the game. She is at home in the air, with terrific aerials and the ability to weave in and out of another person's range. If a Puff is in control, she will hover just outside of your range and poke at you/your shield with aerials. She can poke and weave back without ever touching the ground and thus can maintain control for a very long time. She's got 5 jumps and can autocancel several aerials. With a good read, she can hit you with a pound, a move which stays out a long time and has a wonky hitbox. What's worse, DI'ing any one of her aerials the wrong way is suicide. Puff gets kills off of guaranteed rest setups and DI traps. This is a matchup where you have to learn how to DI each attack. In addition, when Puff is on the ground, her most potent threat against you is grab. Be ready to DI away whenever you get grabbed, because upthrow is the constant threat. If you miss the DI on upthrow, you lose a stock.
So with that in mind, how do we approach these roadblocks as Falco?
First, notice that her grounded options are very limited. Her tilts are good, but situational. Dtilt is a decent poke, Ftilt is a good 'get off me' move, and Uptilt is a combo move. She also has grab and an okay jab. However, because her ground movement is so limited, she can't really maneuver is she's on the ground. So the first step in the matchup is to get her on the ground. The best tools for this are lasers, far and away. Unlike many other characters who are learning powershielding to keep up with Falco's oppressive laser game, Puff needs to stay in the air to maintain control and momentum, so powershielding isn't an option. If Puff takes to the air, she's a clay pidgeon. Reverse laser, runaway laser, do whatever you have to do to shoot the gun until Puff's movement carries her back down to the ground.
Once Puff touches the ground, that's where you take control. Space attacks in the exact same way a Puff would do to you; turn around and autocancel SHBairs until you force a reaction from her. You can also come in with late aerials (dair is good for shield stabbing and nair is good for shield poking) to shines. Her most notable grounded oos option is Upsmash (I think frame 8?), but she gets stuck in the endlag for forty years and you'll get plenty of time to come in with a dair or shine. So, if most Puffs are being pressured into shield they'll be looking for ways to take back to the air. If you have your back turned to her (and you should play a lot of time with your back towards her), you can catch her in the air with a Bair or an Utilt. Be patient, and wait for her to get caught by something you can follow up on.
Once you hit Puff, you actually can combo her pretty well. Dair -> shine -> falling dair -> Uptilt leads to just about anything at low-mid %s. If you're near platforms, you can meet her with a midair shine -> waveland to continue the combo, and on battlefield and yoshi's you can look to kill her off the top with a shine. If you send her horizontally, zone her out with bairs and keep the threat of your dair present. Edgeguarding Puff is difficult, but grabbing ledge and refreshing invincibility is good while you wait for the optimal time to do an invincible shine turnaround dair. NEVER chase Puff offstage, she will always win. Maintain stage control and once you've started comboing her, don't let her reach the ground. Exhaust all of her jumps and keep her unable to refresh them.
To recap. Before you get a meaty hit on her, get Puff onto the ground. Space around her grab and oos options and throw out safe attacks. Once you get a good hit on her, get a combo and keep her off the ground. Then kill her.
