Well I know I'm not as good as Dr.PP but here's a few things I noticed until he gets to it:
edit: he posted as I was typing this O.o
1) there were a few technical errors that I assume you don't want to be bothered about; I'll enumerate if you want.
2) your lasering was inconsistent. For about the first stock it was very good, but you were doing less effective things for a lot of th elater stocks. In my experience, you almost never want to shoot FH or DJ lasers against puff, because they jsut dont do you much good. If she's all the way across screen and you're shooting them to rack up damage or force her to approach is about the only time I find them useful.
The thing is, if puff is at the height where a FH or DJ laser would hit her, and relatively closs, then it's not the best option. You have her at the height where she can't effectively backair or fair or nair you, because she's above your head. Jumping up with a laser puts you at the height where she can hit you with her best aerials all just to land one or two lasers. What you can do is relocate underneath her if you dont like hwere you are on stage, or jump up and bair (or nair if you cant turn around in time, it doesnt work as well but it's pretty decent). utilting works if she's lowish, too.
Actually, more than getting hits off on you when you used FH or DJ lasers, Darc was running under them and closing distance, which isn't usually good to let her do on her terms.
You also approach her sometimes when lasers would be safer... that's more a personal choice, thing, though. if she's in her shield, I usually just keep lasering to annoy her and throw her off her game, but you can approach it, too, since she's not very good OoS
3) Obviously your rest punish was weak. In that situation, dair -> more dairs would have worked pretty well, or just a charged smash.
4) I don't think I saw you utilt at all! Utilt ***** puff's moveset and lets you combo in a way shine doesn't, since it links to dairs and stuff at low-mid %s. If you're in a positionw here you can either shine or utilt, you usually want to utilt.
0:12 was a good time to utilt.
Other than those few matchup knowledge-based things, I think you were actually playing very well. I think especially your first stock was very well played, and obviously your last stock was cut short by you missing a DI, but you were still in it up until that.