ok I went through every character and thought about which moves could hit Kirby after he used Copy, before his shield could come up, and tested them with my brother.
I present to you, The Official-ish List of Stuff that can Hit Kirby out of Copy!
G&W: dair
Sheik: dair
Ganondorf: downb (ouch)
ZSS: dair
Robin: upb
Metaknight: dair (just like in Brawl, it comes out insanely fast)
Fox: downb (that 2% damage punish!)
Lucario: dair
Greninja: dair
ROB: maybe dair (I got it to work one time, and had trouble getting it to work after that, it usually ended up powershielded)
Captain Falcon: downb
Sonic: dair
Everybody: thrown items (bombs, turnips, bananas, gyros, etc.)
Notes: I did not test any customs, feel free to test any you think might be relevant. There were a few moves I tested that I expected to work, but were too slow, such as Bowser Dair/DownB, Diddy UpB, and Pacman's Fire Hydrant. Yoshi DownB gets powershielded every time. I did not test Wario's fully charged Fart, I don't think it works but who knows.
I don't know what the deal is, but it's super hard to get the Dairs to come out in this game. I'm pretty sure in Brawl you could just mash down+A, or down on C-stick, but in this game it VERY OFTEN comes out as a Nair if you don't time it just right. It made it really frustrating to test, but it's good news for us because it means it's hard for people to consistently get Dairs out of Copy, hopefully. I'd prefer if they would just patch it so the move actually has hitstun :/
Most dangerous things are probably Ganondorf/Captain Falcon DownBs, as those moves can KO at higher percents, and it's consistent to do Down+B input, unlike Down+A, but you won't usually be Copying them anyway, so whatever.