Eh no it is not "under" the kraken. people told me that before and I was swimming underneath, wasting my time. Abyssal kraken needs to die, and then there's a blue tag thing that spawns on the island.
Another option is killing the kraken cultist, it's a mini boss that is similar to the world boss Glenn, it spawns on the same days as abyssal kraken, 2pm server time. After he dies, the same tag spawns that you can interact with.
You can interact with both of the tags on one day too, so you could finish it in 2 weeks. The tags stay up for an hour after the death of each (mini) boss.