Arjuna is one of the protagonists of the ancient Indian epic Mahabharata. Why did Arjuna shoot so many arrows when Bheeshma had already surrendered due to the presence of Shikhandi?
According to Mahabharata, Bhishma Parva, SECTION CXIX, Bhishma has not surrendered instead he was only ignoring Shikhandi not all other warriors.
Then Sikhandin, taking up a mighty weapon and protected by Kiritin, rushed impetuously towards Bhishma alone. The unvanquished Vibhatsu then, knowing what should be done after what, slew all those that followed Bhishma, and then himself rushed at him. And Satyaki, and Chekitana, and Dhristadyumna of Prishata's race, and Virata, and Drupada, and the twin sons of Madri by Pandu, all protected by that firm bowman (viz., Arjuna) rushed against Bhishma alone in that battle. And Abhimanyu, and the five sons of Draupadi also, with mighty weapons upraised, rushed against Bhishma in battle. All those firm bowmen, unretreating from battle, pierced Bhishma in diverse parts of his body with well-aimed shafts. Disregarding all those shafts, large in number, shot by those foremost of princes belonging to the Pandava host, Bhishma of undepressed soul penetrated into the Pandava ranks. And the grandsire baffled all those arrows, as if sporting the while. Frequently looking at Sikhandin the prince of the Panchalas with a laugh, he aimed not a single arrow at him, recollecting his femininity. On the other hand, he slew seven great car-warriors belonging to Drupada's division.
Further, next chapter describes how Bhishma had fought till the last. He had not surrendered at all.
Having listened to these words of the celestials, Santanu's son Bhishma of great ascetic merit rushed out at Vibhatsu, even though he was then being pierced with sharp arrows capable of penetrating through every armour. Then Sikhandin, O king, excited with rage, struck the grandsire of the Bharatas in the chest with nine sharp arrows. The Kuru grandsire Bhishma, however, though struck by him in battle, thus, trembled not, O monarch, but remained unmoved like a mountain during an earthquake. Then Vibhatsu, drawing his bow Gandiva with a laugh, pierced the son of Ganga with five and twenty arrows. And once more, Dhananjaya, with great speed and excited with wrath struck him in every vital part with hundreds of arrows. Thus pierced by others, also with thousands of arrows, the mighty car-warrior Bhishma pierced those others in return with great speed. And as regards the arrows shot by those warriors, Bhishma, possessed of prowess in battle that was incapable of being baffled, equally checked them all with his own straight arrows.Those arrows, however, endued with wings of gold and whetted on stone, which the mighty car-warrior Sikhandin shot in that battle, scarcely caused Bhishma any pain. Then the diadem-decked (Arjuna), excited with rage and placing Sikhandin to the fore, approached Bhishma (nearer) and once more cut off his bow. And then piercing Bhishma with ten arrows, he cut off the latter's standard with one. And striking Bhishma's chariot with ten arrows, Arjuna caused him to tremble. The son of Ganga then took up another bow that was stronger. Within, however, the twinkling of an eye, as soon, in fact, as it was taken up, Arjuna cut that bow also into three fragments with three broad-headed shafts. And thus the son of Pandu cut off in that battle even all the bows of Bhishma.
Saying these words, Bhishma, the valiant son of Santanu, as if for the object of consuming the Pandavas, hurled a dart at Partha. Partha, however, caused that dart to drop down, cutting it into three fragments with three shafts, in the very sight, O Bharata, of all the Kuru heroes of thy army. Desirous of obtaining either death or victory, the son of Ganga then took up a sword and a shield decked with gold. Before, however, he could come down from his car, Arjuna cut off by means of his arrows, that shield into a hundred fragments.
Then the king Yudhishthira urged his own troops, saying, 'Rush ye at Ganga's son. Do not entertain the slightest fear'. Then, armed with bearded darts, and lances, and arrows, from all sides, with axes, and excellent scimitars, and long shafts of great sharpness, with calf-toothed arrows, and broad-headed shafts, they all rushed at that single warrior. Then arose from among the Pandava host a loud shout. Then thy sons also, O king,desirous of Bhishma's victory, surrounded him and uttered leonine shouts. Fierce was the battle fought there between thy troops and those of the enemy on that the tenth day, O king, when Bhishma and Arjuna met together. Like unto the vortex that occurs at the spot where the Ganga meets the Ocean, for a short while a vortex occurred there where the troops of both armies met and struck one another down. And the Earth, wet with gore, assumed a fierce form. And the even and the uneven spots on her surface could no longer be distinguished. Although Bhishma was pierced in all his vital limbs, yet on that the tenth day he stayed (calmly) in battle, having slain ten thousand warriors.