"耐着性子看完" can be translated into English as "managed to finish watching/reading it with patience" or "persisted through to the end" (depending on the context, whether it's a video, book, performance, etc.).
Here are some more natural expressions:
"I managed to finish it despite being impatient."
"I stuck it out to the end."
"I persevered and finished it."
Choose the one that best fits your context!