Rider of Red

One of the Servants of the “Red” camp. Though he was deceived by Shirou Kotomine, he understood the situation and reluctantly decided to serve him. A natural-born warrior who, rather than concerning himself over whether or not Shirou's wish would be fulfilled, looked forward to his showdown with Archer of “Black” more than anything else.
His true name is Achilles. The fastest hero among all humanity, lauded for his great valor and prowess in the Trojan War. He definitely ranks equals with Heracles in terms of fame—after all, his name is attached to one of the vital points of the human body.
However, in contrast with his fame, the time during which Achilles accomplished great deeds was comparatively short. His deeds are also almost completely carved into the Trojan War alone. He had the turning point of his life thrust before him at a young age: he could run through his life like a transient gale in exchange for accomplishing magnificent deeds in the Trojan War, or he could become a person unknown to anyone in the world and live a long life.
Achilles gave his answer to his mother without hesitating. “—I will live a short yet brilliant life.”
Achilles was raised by Chiron and, after undergoing training as a hero, he threw himself into the Trojan War. Meeting his sword friend Patroclus, meeting his wife, battles and sworn rivals, meeting Hector—
Without a doubt, Achilles ran through his life while treating all of those things as a joy to have experienced.
He is without a doubt first rate as a Servant. Even among the Servants from Greek legend, he boasts of power that ranks next to Heracles. He also has an abnormally abundant number of Noble Phantasms. In the beginning, all these Noble Phantasms were written out, and when I consulted over how many of them should be used, Mr. NP said, “Isn't a super-strong Servant with an abundance of Noble Phantasms fine?,” and easily permitted all of them to be adopted. I never thought I would end up using all of them…
Naturally, he is a Servant who would instantly run out of mana if he used them in a normal Holy Grail War. The mana consumption of Rider's chariot is uncommonly harsh in particular, and only a first rate Master could fully utilize him.
Additionally, besides the Rider class, Achilles has aptitude as a Lancer, Berserker and, quite unusually, a Shielder. His complement of Noble Phantasms is slightly different in each of the other classes. For instance, as a Lancer, he would lose his chariot since it is his Noble Phantasm as a Rider, but his spear would gain the secondary effect of causing HP reduction.
His fatal weak point, his heel, serves as the linchpin for his Noble Phantasms “Andreis Amarantos: Amaranth of the Brave,” which maintains his immortality, and “Dromeus Cometes: Comet Form,” for which he is extolled as the fastest, and when his heel is pierced, these two Noble Phantasms disappear. After being pierced once, it is extremely difficult for his heel to be healed, and, without the use of some extraordinary means, there is no way for him to completely regain his running speed afterwards.
In this Great Holy Grail War, Achilles wished for a showdown with his teacher, Archer of “Black,” and gave his assent to Shirou Kotomine's actions for the sake of accomplishing that. This might be because, leaving aside his animosity towards Semiramis, he does not really hold much ill feelings towards Shirou. Just as Archer of “Black” aptly pointed out, Achilles is naïve when it comes to his recognition of enemies and allies. This is a probably demonstration of the difference of experience between him and the older Cu Chulainn, who is able to decisively kill when he needs to kill even when split between enemies and allies in such a manner.
His connection to Atalanta actually begins from a story he heard from his father in life. His father, who was always somehow gentle and could never stand up against his mother, had spoken of his encounter with Atalanta embarrassingly, and because of that the young Achilles always remembered her. He never got the chance to meet her in life, though.
Achilles thinks that it is his fault for overlooking Atalanta's transformation while engrossed in his own battle. He fought her in her rampage as a way of atonement. Achilles cried out of guilt for having crushed Atalanta's dream.
But I'd like to think that it was that very naivety and tears of her that granted Atalanta a small measure of salvation at the very end.

Fate/Apocrypha material: Fate/Apocrypha Encylopedia