Since both languages are not my native ones I had to find my reasons in dictionaries as I did not know the answer off hand. The dictionaries said tener duro = to persist etc. Having a second look at your question: you could be right. A very roundabout way of checking that would be to use feedback. If Duolingo accepts it, you will get a mail confirming that.
This is one of those set phrases with a lot of different translations, giving a good chance that many valid translations will be missing from the database. (I had to guess three times before I hit something that Duo approved of). So, to anyone reading this discussion because Duo didn't accept their valid answer -- please report it, and be part of the solution!
A reference which confirms that the vocative should be indicated by a comma in English: https://www.grammar-monster.com/lessons/comma_with_dear_hello_and_hi.htm
"Hold fast," is a command given to sailors hauling on a line. "Hang on tight," is certainly used, but "Hang on tightly," would be more correct. "Hold firm," and "Hold tightly," are things you do with a belief or opinion. "Hang loose," (relax) and "Hang tight," (wait a minute) are 1950's slang.