I myself have encountered the Kraken 3 times.
2 times on a slope (by myself)
A third time on an open galleon with 3 other people (who were y fortunately noobs at the game)
When you first encounter the kraken, you will notice that the water will get incredibly dark. (That might be ink, no one really knows)
Once your done with the Adrenalin you get from seeing that, you will start to see tentacles rising up from the inky water. The tentacles that are closer to the water (and squirming around like maniacs) are “active tentacles”. Those are the ones that will suck up your crew mates and deal damage to your ship. You want to take them out as soon as possible.
Note: the tentacles take the most damage when they are trying to swallow your crew. When they open their mouth mouth, shoot a cannonball right in the middle!
Now, once the Kraken gets bored, it will then move one to the next boat (or disappear).
You can’t really kill the Kraken. If you try going underwater (you will take damage from the inky water, FYI) you can’t see the Kraken, you will just see black. However, when you “defeat” the kraken, you will get an achievement: “Kraken good time” (something like that)
Here is a video!
https://m.youtube.com/watch?v=lclQNHRmv6c
Now, weird thing is, whenever I encounter the kraken, I always have a cursed skull with me. I am not sure if this has anything to do with the Kraken, or just bad luck.
Hope this helps! -jazapple