@Loaf:
Basics:
Use bair to momentum cancel, it's faster then uair. Don't ever use firebird as an attack. If your opponent is far away and you're just doing empty shorthops, do SHL or SHDL instead.
Other:
You can do something besides drop down > jump > phantasm as a ledge option, you know. At one point, your friend was standing at the middle of FD, completely telegraphing the fact that he knows you'll phantasm. You got grabbed soon after =D
Don't spam usmash when he's NEAR killing percent but not quite there yet, especially since he's Lucario. The way the stale moves system works, if he's at 110% and you use your usmash but he doesn't die, you now have to use 2 other moves besides usmash or land TWO more usmashes for a kill. Since he wants more damage becauase he's Lucario, you're screwing yourself over completely.
Moar lasers. Moar IAP.
Learn to time the dair so it spikes, I think you only had 2 succesful spikes out of 10 or something attempts. It usually isn't worth it to try unless you have a VERY good opening (intuition or practice, sorry). Examples: 1:13, 1:43, 2:43, 8:27, etc. If you don't feel you'll get punished use bair instead. If you simply insist on using dair though, then always do a rising dair rather than jumping off dair (rising dair as in walk off the ledge, move towards him slightly, then use your 2nd jump and dair as you're coming up).
And then one specific thing: at 8:45, you could have potentially won. If he doesn't tech like that, don't use dsmash, he has invincibility. Put up your shield and see if he attacks it (a smart player won't, but who knows).
You also said you wanted strings, try dair at a percentage where they bounce into the air then do dair > uair (staple move). Nair > jab > something if for some reason you hit them with nair is good, and see if you can incorporate reverse boost pivot grabs into your game, there were a few oppurtunities like 1:57ish and 3:36.