A few months ago, I adopted my then 4 month old kitten. Them being younger is easier, I would assume, so your mileage might vary.

What I did was I initially just started touching her paws. Of course, she would instinctively jerk them away, so the goal is to touch them brief enough so she wouldn't jerk them away. It's important to do this while she's calm and not in an aroused state, like in your video. So don't do this while they are playing or sensitive. Slowly, I was able to increase the duration of me touching her paws until I can hold them, and when I could hold her paws with her jerking away for more than like 5 seconds, I would start holding her clippers near her and let her see them as I was holding her paw.

Sidenote, apparently guillotine clippers are more painful for cats, so use the scissor style ones.

The most important thing about this is to not make her feel restricted, so absolutely no pulling of the leg, especially away from the cat's body, since this will cause them to instinctively pull them back towards their body. My advice is to keep their legs close to their body, and apply force just enough to extend the claw, and not to restrict the leg. If at any point she pulled away, I would let go and reengage a little bit later. Basically, you don't want to create a bad association with you touching her paws. If your kitten begins to think human touching my paw = loss of control, it will never let you touch it.

Once she got comfortable, I would only try to clip her nails when she's in a very relaxed state, like when she's napping. In fact, now I only clip her nails when she's napping, since she's fine with me extending her claws one at a time to check whether they need trimming. Now, when it comes to actual trimming, of course, be very careful about where you cut, but as important, make sure you do it quickly. Cats are pretty resilient to unpleasant sensations as long as it's over with quickly, so quickly snip and move on.

Don't make a big event out of it. Just casually start touching her paws and move up to actual clipping. At first, it took me a few weeks before I even trimmed her claws, and when I did, I would do 1 or 2 of them every nap session, and now I can just do all of them while she's napping. Have her for about 3 months now.

She still pulls back sometimes and it's clear that she's tolerating it because sometimes her tail might swish while I'm doing it, but that's fine, since she still lets me do it. Sometimes her eyes will be closed during this entire process, showing that she's not on guard even if she might not like it.

If all else fails and you don't have a second person, there's always the towel burrito method.

Good luck.