Learn English – have difficulty vs have hard time vs have trouble vs struggle

I would have selected 1 and 5 as well. (Note: I am not a native English speaker.)

A struggle (in the sense of an effort, rather than a fight) is usually described as difficult. It feels a bit strange to talk of a large struggle. Since arduous means very difficult, “arduous struggle” is a perfectly natural superlative: choice 1 is definitely correct.

“Herculean struggle” is also correct because “Herculean” can have two meanings: big and strong like Hercules, or difficult and strenuous like his labours (tasks). One would usually say ”… remains a symbol of a Herculean task“ though.

Colossal means very large, so it feels unidiomatic to talk of a “colossal struggle” here, though I think the phrase would be understood without trouble.

Statistics show that “arduous struggle” is definitely idiomatic, and “Herculean struggle” and “colossal struggle” are markedly rarer. The peak on “colossal struggle” starting in 1914 seems to be due to descriptions of World War I, with struggle meaning a fight rather than an effort (justifying the description as large: it's a large fight because it involves a lot of people).

These don't mean the same thing.

"Barely managed" means "he struggled and succeeded by the barest margins". It usually implies the problem was with his capacity to do the work itself. "Had a hard time" has a more general meaning, like "he had some problems while doing something". It doesn't suggest anything about how well he did, nor what the problems were.

For instance, a single parent with financial troubles and no support from their family would likely "have a hard time" completing a degree, and might take ten years to do so, yet still get very high marks and never doubt that it would get done. This is not someone who "barely managed".