If someone asks you what you consider to be your most important achievements of the past year in an interview, what they're really asking is "What have you done in the past year that you think we'll be most impressed with".
For example, finishing Flappy Birds or buying a new apartment in GTA V might be a pretty big achievement to me, I might even care about it more than academic or work-related achievements if I'm passionate enough about these games.
But disclosing that kind of information in an interview will likely result in a negative reaction.
Instead, you really have to think hard about what the interviewer would like to hear.
For example, if you're applying for a job as a web developer, you could say something like "I recently got to grip with the latest computer programming language, and it has opened up all sorts of opportunities, made my code tidier and allowed to me to create better applications in a shorter space of time.
Basically, think about what would be an important achievement in your professional field, and then try and apply that to your experiences in the past year.
My biggest achievement is passing my exams without studying very much like my colleagues...