You cannot stay in one place when Puff has center stage, her back air walls will beat the priority on mostly all your moves. The best solution I have noticed so far is to gamble by aggressively approach with wave dashes, and (rarely) dash attack.

When Puff isn't getting heavily pressured, your dash attack will get easily punished by good spacing, but it's always good to use it as a 1/10 mixup to wave dashing.

The best approach is wave dashing forwards and backs to catch Puff slipping, and either trade/get shield pressure/raw hits with tilts and jabs. Getting under Puff is a lot better than being behind her or in front of her when she has center stage.

Mix homing/fast missiles when you have center stage and Puff is recovering, and prioritize charging your Charge Shot. Any extra damage you can get on Puff will pay off, and Charge Shot will give good kill threat and will whittle down her shield for approaching with tilts and jabs.

Crouch cancelling is a must to get stage control, but CC down smash is very weak in this match up.

For your neutral aerial to be effective, it needs to be out before Puff's hit/hurtbox approaches you, otherwise her back aerial and forward aerial will always beat you. Fast fall back aerial when Puff is grounded is very weak in this matchup, but stray hits with back air and nair keep Puff honest and are rarely punished if you throw them out before Puff approaches you.

Never approach with fair, always use wavedash tilts/jabs.