Arjuna used Shikhandi as a shield

Bhishma also took an oath to not kill any of the children of Pandavas Bhishma had taken oath to not leave the field of Kurukshetra when he was doubted by Duryodhan and even decided to kill Arjun the next day (9th day of war) who did not even want to fight Bhishma :his Pitamah. But knowing this Shri Krishna sent Draupadi (wife of Pandava's) to the tent of Bhishma. Bhishma blessed her "Akhand Saubhagwati Bhava" then he realized about his previous promise with Duryodhana of killing Arjuna and he also knew it was Shri Krishna's plan to break his promise so he said to Shri Krishna "You broke my promise or I'll break your promise of not taking any weapon during Kurukshetra battle".

Bhishma made Arjun go in pain since Arjun did not make ant serious attempts in countering Bhishma but he did not kill, he made made every attempt to make Krishna angry on Arjun and raise weapons in his defense but in result Shri Krishna raise a wheel and even Arjun begged in his feet to forgive him vowed to kill Bhishma in hurry, though Bhishma felt relaxed for a second but soon he realized how wrong he had been for so long .Then the true fight started and Arjun stunned Bhishma till the sunset.

After hearing that Shri Krishna had to lift a wheel as a weapon in the presence of the great Arjun he went to Bhishma’s tent and he saw him injured and weak than ever before Bhishma told told Yudhishthir that he won't attack on a person of opposite gender and thus could be defeated. Why weren’t women allowed in the war?- Because during the discussion of the rules of the Shakuni knew what could happen if women were allowed to take part in the war, pandavas had many talented women warriors like Draupadi, Kunti, Subhadra and etc, thus he told everyone how brutal was the war going to be and convinced everyone that women should not be allowed to take part in the war since mother are only one who can take humanity further and propagate Dharma, anyone who killed a woman shall be punished .

Yudhishthir instantly understood that he was talking about Shikhandi who had become a man for a single day, though Arjun had given a tight fight to Bhishma that time but still could not sleep because he could not imagine penetrating his Pitamah's virgin body. The next morning Yudhishthir came with the plan of keeping Shikhanda (Male of Shikhandi), every person of the Kaurava army would see him as a male but Bhishma who knows her from her previous birth of Amba had seen him as a woman.

Initially Arjun refused to use such tactics but Shri Krishna knew that Arjun’s soft heart would not let him do so ,he needs some kind of start from someone else, Shikhanda the told them about her boon that she shall be the reason of Bhishma’s death, Shri Krishna convinced Arjun keeping her on his chariot they began marching towards Bhishma who was surrounded by Dusshasan and other groups of Kaurava soldiers. Arjun cut every arrow and attack towards them but did not hurt Bhishma, when Shikhandi injured Bhishma a little, Arjun stretched this bow with a sigh and then fought Bhishma. Bhishma used all of his force and weapons available but Arjun cut all of them and then at the end penetrated his Body with multiple arrows .

Bhishma could show his power as long as Arjuna looks on without countering him with his full mettle. But if Arjuna comes into his element like he did on 10th day ,Bhishma could do nothing at all. Even before that Bhishma had no reply for Arjuna’s Aindrastra that created havoc. It was not Arjuna but Bhishma himself who had planned this with Yudhishthira. Arjuna or Shri Krishna never suggested or planned that.

Original plan was to put Shikhandi at the head of Pandava army and Arjuna and Bhima protected him from right and left flank. Shikhandi was on his own separate chariot. He was given the task of bringing down Bhishma. And neither was Bhishma alone he was protected by Dushasana and several other Maharathis. But as Shikhandi was not able to bring Bhishma down here then Shri Krishna told Arjuna to bring down Bhishma himself.

Arjuna them first killed all his supporting warriors and defeated Dushasana and made him weaponless . And here Arjuna shot at Bhishma from such a position they for some time all felt it was Shikhandi who was striking him. Arjuna severed all his bows them Bhishma grabbed spear and attacked Arjuna but Arjuna shattered it and then Bhishma tool sword and shield but Arjuna shattered that too and here when Arjuna fired arrows on Bhishma body Bhishma realised it were arrows shot by gandiva by the amount of pain it caused and he said the same to Dushasana there who was watching all helplessly that those are arjunas arrows. So he brought down Bhishma fairly as neither Bhishma was unarmed and nor unaware that he is shot by Arjuna.

Bhishma himself was reluctant to fight for adharma and was tired of listening to Duryodhana's allegations of being biased towards Arjuna, the each time he got defeated. Arjuna was capable of defeating Bhishma but in Kurukshetra, merely winning over the latter was not enough. The situation demanded that Bhishma should at least be made incapable to fight as he had ichamrithyu. Bhishma himself told him the way to defeat him forever which was to bring Shikhandi. Though Shikhandi had shot arrows at him, the arrows didn't do any damage to him. Though they were in the same chariot Shikhandi was fighting other in different directions. Bhishma did fight Arjuna and his weapons got exhausted.

No one could defeat Bhishma, till such time that he was having a weapon in his hand, he was an exceptional warrior. Bhishma wouldn't give up weapon, without a valid reason as his loyalty always lies with the crown of Hastinapur. But, it's his personal policy to never fight with a woman, but a woman cannot enter the battle field of Kurukshetra (at least not when the war is going on) So, someone of middle gender was the only solution. But, I believe it all has greater meaning in the bigger picture. Shikhandi was born only to kill Bhishma, so it's simple really, she had to fulfill her purpose. Jay Shri Krishna