Excuse me while I turn into Mekos.
Just in general in doubles, if you're Toon Link then it's your job to NOT directly fight anyone if you don't have to. Play a keep away game, hold stocks, look for opportunities to follow up on your partner's actions (be that team combos, shield pressure, etc.), and keep an eye out for when your partner needs help.
That last part is crucial, so I'll give you a few early examples of when you could have done it. At about 0:30 your partner starts getting hit by Zelda's dtilt over and over. You were in perfect position to punish (literally right beside Zelda) and get your partner out of it, but you let it happen, focusing on Falco the entire time, and eventually your partner just dies, with no punish on Zelda from you at all. Not long after that, your partner is getting chaingrabbed by Falco. Again, you are in perfect position to stop this, but you let it happen and he takes way more damage than he should have. Looking out for situations like this will save your team from A LOT of potential damage, and set the other team up for taking a lot of damage themselves.
Lastly, if you need help with ANYTHING, don't be afraid to just tell your partner to come help you, and make sure your partner knows that they can ask you for help too.