Try not to b-reverse so aggressively against Mario, he'll gladly answer it with a bair every time. Although your little dance over Chrom at the end was beautiful, it only worked because he started panicking for the kill.
Battlefield is an awful choice against Yoshi in general, but it depends on the player. Nikes wasn't overly campy, so he had no problems rushing you, and both of your last stocks were because you got caught on a platform. If the Yoshi is really egg-happy, then maybe, otherwise I'd sooner recommend Final D again.
If your Aura is as high as it was at 8:38 (vs Nikes) and his shield is that low, honestly, I'd probably start spamming Force Palm. You're hanging by a thread with a stock to spare anyway and FP isn't awful at breaking shields. If he messed up his powershield, it would have been gg (unless he just took it, of course)
Use grab more.
Decent play and movement in general, but you need to play the MUs a bit better and tighten up your punishes. Learn which attacks are safe on shield and then don't punish them with Force Palm, much as you really, really want to.