Interesting, but tough question! Naturally mine is biased towards the things I am interested in/passionate about!

1> All time greatest achievement - Travel (boat, air, land) and communications. We've expanded so much due to our abilities to explore the world and communicate with others outside of our immediate areas

2> 20th Century's greatest achievement - the automobile, the phone, or the 'net- oh yeah, and medicine

3> So far the greatest achievement of 21st Century - Well there's not much the past 9 years that really stands out to me... the election of a minority president is huge.

4> All time worst achievement - Ever in history? Wars (including WW2)

5> 20th Century's worst achievement- I'd have to agree- the Holocaust and similar events which are less talked about

6> So far the worst achievement of 21st Century - War will win this one again, for me