Really solid movement.
Maybe wait onstage before you grab the ledge, long enough so that you can see if he is going to go high or low to recover. As soon as you got him offstage you grabbed the ledge asap, which is great for low recoveries, but when he went high, it took you too long to get to him and couldn't always maintain the edgeguard.
Be more aware if Falcon can double jump to grab the ledge, or if he will have to use his UpB. Sometimes when he could grab the ledge before you could reach him you would start throwing out attacks, even though he was safe, maybe you were hoping he would try to air dodge on or use his UpB?
You might want to try being more defensive when he has good positioning or invincibility, at one point you put yourself in a hole on PS when he was invincible, which I think is a pretty bad option. Also, when you were put in some awkward situations after that you would throw out aerials, but weren't in a position to follow them up, such as when he randomly jumped on the tree at 5:10, and you caught him with a D-air at low %s, and landed on the tree which was below and in front of him. You then did a DJ N-air and nearly got stomped, but then got U-aired. It was all really awkward. . .
Be more careful with your DJ, you threw it out quite a bit, and it often caught him off guard, but if he gets you you're in a horrible position. At one point you dropped off the ledge and shine stalled to lose your invincibility then went up with a U-air and got kneed. . .
Toward the end I think you were confident that you had it and started getting greedy, and lost an edgeguard because you started charging a F-smash and he simply UpBed over you to safety.