"耐着性子看完" can be translated into English as "endured through to the end" or "patiently finished watching/reading (it)".
Here are some example sentences to illustrate the usage:
1、 I endured through to the end of that boring movie, even though I wanted to leave halfway.
(我耐着性子看完了那部无聊的电影,尽管我中途就想走。)
2、 She patiently finished reading the long and tedious report.
(她耐着性子读完了那份又长又乏味的报告。)
The first phrase "endured through to the end" emphasizes the act of persevering despite difficulty or boredom, while the second phrase "patiently finished watching/reading" highlights the patience exercised in completing the task. Choose the one that best fits the context.