Some quick pointers:
Be more aggressive when you land your down tilt. You can often follow them up with grabs or more down tilts.
When he Forward B's your shield while you're facing backwards, don't back air out of shield. It has poor knock back in those situations and it can be too slow most of the time. Use a short hop neutral air out of shield instead to create a platform/ground techchase.
Use Down throw a little bit more on platform stages, even at low percentage as they'll create more tech chase opportunities. Also use down throw when you're facing away from the stage (at 2:19) instead of back throw since they'll often DI back into your down throw and you can get a kill combo from that, or they'll DI away from the down throw and you can edgehog and THEN you use back throw to throw them after their laggy recovery.
If they try to recover low while you're on the edge, then you can pursue them with your back airs.
You're throwing out Up Smash a lot, I'm not sure if it is intentional or not, but you typically don't want to use that move until they're at a percentage where they won't punish you for getting hit. Up Tilt under platforms is much more efficient at almost any percentage. Up Smash has more utility on a stage like FoD than even Yoshi's Story. It just gives you that surprise last hit like on Pokemon Stadium, but most of the time people will shield the whole thing even if they're not getting hit immediately out of fear/instinct.