His life is interesting in the sense that people hate him because of his penchant for unbridled brutality. He's hated because of the life he's chosen for himself and the focused way in which he carries out his abominable acts. Chigurgh's interest is money and his is a lifestyle that concentrates on getting significant money by illegal means. His hope is to make a substantial amount of money without working for it in an ethical way. In essence, he's looking for easy money; however, his path - in the book and in the film - to attaining wealth turns out to be not such an easy way to riches.
His strength is his relentlessness in pursuing his goals. His weakness is his lack of morals, which in the end, will eventually be his undoing, albeit in another time in this fictional life. His achievement, in a perverted way, is his winning his battle with Llewellyn. His failure is his inability to see that what he's doing is wrong. He's convinced himself he's doing what is right according to his weird set of values.