The critic found that few films lived up to his satisfaction this year.

to 在这里是介词，表示"达到某种标准或程度"。 his 是代词 he 的所有格形式，表示"他的"。 satisfaction 是名词，来自动词 satisfy（使满意），意思是"满意、满足"。 live up to his satisfaction 这个短语的意思是"达到他的满意标准"。