Most important ,perhaps ,was that they had all maintained with a certain fidelity the technique and composition consistent with those of America's first popular landscape artist ,Thomas Cole ,who built a career painting the Catskill Mountain scenery bordering the Hudson River.
抓主干：
That was important
解析：most important为形容词置于句首后紧接系动词可以判定为倒装；
主*顺序应该是:that was most important.而they had maintained with a certain fidelity the technique and composition consistent with those of America’s first popular landscape artist ,Thomas Cole ,who built a career painting the Catskill Mountain scenery bordering the Hudson River.为主语从句，在翻译的时候先翻冗长的主语从句。
析枝叶：
主语从句的主干:1.they had maintained with a certain fidelity the technique and composition（注意with a certain fidelity做状语）
2.consistent with those of America’s first popular landscape artist（做后置定语修饰technique，consistent形容词，与…相一致）
3.Thomas Cole做同位语
4.who built a career painting the Catskill Mountain scenery定语从句修饰Thomas Cole其中painting.做career的后置定语
5.bordering the Hudson River后置定语修饰scenery.
译文：他们都几乎忠诚地在坚持着和美国第一个流行景观艺术家托马斯.柯尔的技法和构图原则一致的技法和原则，这是很重要的。柯尔一直在从事着描绘哈德逊河两岸的Catskill山风景的事业。
