It's the 6th time that I'm trying to defeat Kayran. I looked for this bug on the Internet, but still can't find any solution. I trap the tentacles in Yrden, I try to chop them off, but Kayran's health goes down a bit and then it comes back up, infinitely. I have no idea how to solve it, I've tried loading previous saves, restarting the game, nothing helps.

You said that you Try to chop them off, right? You did not actually cut any of them during fight? Maybe you are getting to them too slow, or you are using steel sword instead of silver one, so you arent dealing enough DPS to cut tentacle in time?

PS: By the way, If your version of game is not fairly bought, read - pirated - it's included such as a lot of "easter eggs" will happen during game making you die in strange moments or be unable to defeat monsters, making game experience quite low. Just saying.