A lot of years ago I liked to answer the question about my greatest accomplishmeny by saying I achieved the impossible. It usually made the interviewer's expression shift noticeably.
The story behind it related to some hardware that a particular company supplied, that was a real hassle to manage centrally. A friend and I had worked at a place that used them, and asked the company whether they offered some software to control them. They said it wasn't possible to control them with software. Logic said it had to be possible, so my friend built a hardware doodad to control them and I wrote the software to pair with it. And, lo and behold, what was described as impossible came to be in the space of a couple of months.
The question about your greatest weakness is the sort of thing that seems to have no right answer. The person who says they have no weaknesses shows an arrogance that is unlikely to help but admitting to a weakness provides an easy excuse for an interviewer to throw your resume in the trash and move to the next candidate. Some say the best answer is to acknowledge a weakness and demonstrate how you turn it into a strength. I haven't interviewed in years so don't know how well it would work these days but I often brushed the question aside with an answer, offered as a half-question, along the lines of "a disinclination to shoot myself in the foot?" Usually it seems to have been taken in the spirit it was intended.
