You now need to go back to Citra at the temple, so fast travel there and head to the marker. She gives you some poison to drink, mentioning that only the strongest will survive. You will see a giant shadowy figure appear from behind the building, and you will have to fight it!
You get an unlimited amount of explosive arrows for this section. One of the first attacks the beast will do is lean down and spit gas, which will leave behind fire where it lands. The mask is the weak spot, so that's where you need to shoot. Keep doing this until it disappears and the area gets dark. Some smaller shadowy appears now appear, who will rush and try to melee you.
Keep killing them by shooting them with the arrows and if you get any chances for an instant Takedown, do it. Your best option is to not aim and just shoot at the ground near them. Once you kill enough of them, the Ink Monster will reappear and the second part of the battle will begin.
The Ink Monster will now throw some giant balls at you, and the best way to avoid these is to just run from one side of the arena to the other in a big circle. Every three balls, the monster will stand still, which is your chance to take a shot at the mask. Once enough hit have landed, the monster will try one more breath attack, then it will be finished. Run up the arm and follow the QTEs until you kill it, then enjoy the cutscene as the mission ends.