"What is your biggest achievement?" and "What was the hardest challenge in your life and how did you manage it?" are quite good questions.
Just be honest and use the STAR structure to make your answer clear and full.
S - describe the Sutuation (achievement or challenge).
T - Tasks you had to manage.
A - your personal Approach to the sitruation and what exactly you did to solve it.
R - Result of your efforts and the final outcome. Also, what you've learned out of it.
Hope this helps.