This is an idiom describing someone’s walking manner. Usually,When a man is extremely arrogant or cocky,he is very much likely to hold one's head high and walk in vigorous strides with big steps,throwing his weight around,just likes a cock. So,"walk with one's head high" holds the equivalen meaning as “Be on the high ropes”.

如果一个人非常骄傲和自负的时候，他走路时通常把头高高昂起，把脚抬得很高，显得神气十足。“趾高气昂”这个成语就是用来形容一个人骄傲自满，得意忘形的样子。

趾高气昂 (Zhǐ gāo qì áng)
【翻译】walk with one's head high.
【释义】趾：脚趾。昂：高高抬起的样子。形容一个人骄傲自满，得意忘形的样子。
【例句】自从她的丈夫被提拔为单位的主任以后，她一天比一天骄傲起来，连走路都总是一副趾高
            气昂的样子。
【近义词】得意忘形、得意洋洋
【反义词】灰心丧气、无精打采、灰头土脸