It looks like you need to work on spacing you aerials. She has ridiculous maneuverability, you were hitting him (of hitting his shield) and hanging out in this range. . . don't do that. You have to hit and run constantly, get in, get out. If he starts to excessively spotdodge, use pound.
Great job with the grabs. Good offstage presence as well, I like that.
The first thing is the biggest, learn her aerials. No disrespect, but they looked absolutely clumsy to me. I know you're better than that, jsut unfamiliar with her. You want to always be hitting with the tip of the moves.
Also, you were approaching a bit too straightforwardly. Wokr on jumping in and baiting your opponent, eat through their reaction with pound. Slowly advance with airdodges and crouches, and be prepared to jump high up and wait it out. Patience is rewarded with Jiggs, she does exceptional numerical damage and kills early, you don't always need to be the aggressor to be successful with her.
It's hard against Falco because of lasers limiting your options and forcing you to approach a bit a slower, so I'd love to see some vids against other opponents, I think I could give a bit better advice if I saw you on a character that allowed you to be a bit, how shall I say, freeform.