It depends on what you mean with "during difficult times". Is it "during (some) difficult times" = "pendant des moments difficiles"? Or "during (all) difficult times" = "pendant les moments difficiles"?
You could translate "I had (some) difficult times" with "J'ai eu des moments difficiles" and even in this sentence it would be an acceptable translation in my opinion but I think they wanted you to understand that those are Léa's difficult times, definite ones, and not "some difficult times".