This is your opportunity to sell yourself to the interviewer. Make sure that before the interview you have checked out what is required in the job. Before the interview think through the skills and achievements you have that match the skills required in the job. When you are asked this question you can then sell, sell, sell yourself for the job.
In the links below I have put a guide to interview success that tells you how to structure you answers.
http://www.tonygoddardconsulting.com/career-coaching/interviews-success/
The key is in the time spent in preparation. This means you can be confident and polished on the day
It is the greatest achievement of a teacher when his/her work is valued the best by her own students even after so many years.
The greatest achievement of the Inca empire was the building of Macchu Picchu.
This is a common interview question. You could say your greatest professional achievement was to help transform a policy or a department or to encourage your team at work. There are many things you could say, just be honest and creative.
Bobby Orr's greatest achievement ever was that he was a defenseman with an offensive mind.
The greatest achievement of any gay person is to live a happy, healthy life.
Designing to respond to clients while still maintaining good design and integretity in my work.
The greatest achievement of the Han Dynasty was the seismograph and the art of making paper.
electricity
your birth
His temple
He considered his lifelong greatest achievement (when asked at around 86 years of age), lifelong celibacy.
Her greatest achievement was saving john smith and making her live better