I play against who I believe is one of the smartest players on the west coast, MogX. His kirby has beaten people like SK92, mikeHAZE, BarDulL, and Mike Hey in tournament. Many consider him the best Kirby on the West Coast, and if you know who tImmy is, an influential Kirby player on the Kirby boards, MogX beat him in doubles. I'd say I have a handle on the match-up and I'd say I'm even against him if I play with absolutely no mistakes.
(Sorry for the long-winded introduction, but I feel its necessary to present evidence that you have at least some knowledge of what you're about to say. You can't judge how good a person is until you can list who you've beaten and who they've beaten. If it sounded arrogant, that was not the intention. I don't think I'm good, I play Lucas.)
From the beginning of the match, to the very end, as any character you must watch out for Kirby's grab. Any good Kirby will grab you, down-throw you, up air afterwards, re-grab, etc until they combo you to around 40%. This is almost inescapable and your best bet is to Smash DI or normal DI up and away from him. Kirby's grab range is disjointed and very long and is also very quick. If he is near you on the ground, this will most likely be the approach of choice.
Grabs are safe immediately out of shield, so at your early percentages if you rush into a shielding Kirby, I'd imagine you're going to get grabbed. Also, since most character approaches involve a character running in, dash cancelling into a shield, do not run in to intercept a running Kirby. It's best to jab then jab-cancel into a retreat, or stand your ground and f-tilt, and hopefully you spaced it properly so that the very tip hits, Kirby shields and is pushed back a tiny bit, and he can't grab you.
In the mid percentages, Kirbys will still try to get you into a grab for the d-throw damage (no combo after with proper di) and they have many options to do so. If you find yourself face to face with a Kirby in close range, your best bet is to jab. You can also dtilt to fsmash. The dtilt option should be done at later percentages and sparingly because usually it's a surprise KO more so than a spacing tactic. But in the early to mid percentages, when a Kirby is in the air avoid approaching from directly below him. Nothing you can do will stop his dair, and it auto-cancels, so a Kirby can dair to ftilt, or dair to grab, or even dair to fsmash and kill you early if you do not DI and you're caught off guard.
In the higher percentages, Kirby's are usually more vulerable than you because of their light bodies. So, a smarter Kirby will space and be in the air where they have more of an advantage. Be careful, because a Kirby on the ground may run at you, but instead of any ground attack, they'll RAR into a bair and you'll be tempted to attack but best just retreat and PKFire.
Although Kirby's are strong in the aerial department, their horizontal mobility is nothing when compared to characters like Wario or Game and Watch. To travel the same distance horizontally, they'd have to expend jumps. And since their best horizontal aerial approach with Kirby is bair, all they can do is slowly inch their way toward you. Abuse this by jumping up and intercepting them with one PKFire. Do not PKFire them in the air more than once unless they expend all their jumps. There are 5. Count them.
Bair does not come out as fast as you think. There is a notable start-up lag to the move, so a Kirby already dedicated themselves to the move after completing it. So if you expect a bair, just stay away, and the second comes out, you have a good half a second window to punish with a fair (rising into the air, never falling), or an uair which cancels out all of Kirby's aerials save his nair (which they should never use) or his dair. If you can predict how they'll land by counting their jumps, punish that with a nair by waiting for them. But watch out, Kirby's like to sneak in one last bair before they land. Wait for the complete landing, then nair.
Punishing Kirbys is tough. Kirby's have excellent tools for spacing, and sometimes all they need to do is rely on all the moves that outprioritize yours. Your best bet is to follow their patterns. Know when a Kirby lands, and memorize the flow of their "combos." Kirby's lead into a fsmash after their so run just far enough to avoid the follow up fsmash, then counter with a fsmash of your own. Or, if you're brave, wait for the last hit of the dair, then uair. The kill potential of uair is understated and it works great to get a kirby away from you. Ftilt helps on a kirby approaching from the ground, and rising fairs, never falling, always serve as good punishers when a kirby is about to finish an aerial in front of you.
That's it. I have more but I have to study for finals. Peace.