Lums are the yellow things which you can pick up during each level. Each coin equals 20 lums, and the normal yellow lums equal 1 lum. Each level has 100 lums which you can collect. You can replay each level to collect more lums, or simply play more levels. 1000 lums should be very easy to collect, because just the first level already has 100 lums. You can replay the first level 10 times if you find the other levels too challenging.
Be sure not to spend you earned lums, as you need to have 1000 lums "in cash".
On your way to this achievement, you will have earned: