Swim your tame next to it and wait for the grab, dismount and feed the pearls then swim up, it will do around 2.5k damage before it lets go of your tame so keep that in mind when deciding what to take.
Rinse and repeat
Use a Mosa to tame this beast. Let the Mosa get grabbed wait a couple seconds get off feed it black pearls. Have your mosa on follow lowest, swim a bit away from the Tuso after feeding it, when the Tuso lets go the Mosa will swim to you. Repeat until Tuso it tamed. Super easy!
You need two people, one for feeding the black pearls and the other to feed the turtle that is in the grasp of the Tusoteuthis, with sweet vegetable cake for the health and to feed it stimulates berries as well